Patients with history of John Cunningham (JC) virus identified in the cerebrospinal fluid (CSF) or previous history of PML will be excluded from the study Patient must be CNS (cerebrospinal fluid [CSF]) negative for leukemia Patients with evidence of metastatic disease will be excluded; any evidence of non-contiguous spread beyond the primary site as determined by pre or post-operative magnetic resonance (MR) imaging of brain, pre or post-operative MR imaging of the spine, and post-operative cerebrospinal fluid (CSF) cytology obtained from the lumbar CSF space (the requirement for lumbar CSF examination may be waived if deemed to be medically contraindicated); CSF cytology from a ventriculostomy or permanent ventriculoperitoneal (VP) shunt that reveals the presence of tumor cells is indicative of metastatic disease Patient must have negative lumbar cerebrospinal fluid (CSF) cytology; CSF cytology for staging should be performed preferably no sooner than days post operatively to avoid false positive CSF; ideally, CSF should be obtained between day and day to allow for final staging status before enrollment onto the study\r\n* Note: patients with positive CSF cytology obtained prior to days after surgery may have cytology repeated to determine eligibility and final CSF status Patients with metastatic disease by either MRI evaluation (brain and spine) or lumbar CSF cytology are not eligible; patients who are unable to undergo a lumbar puncture for assessment of CSF cytology are ineligible Lumbar CSF must be assayed for cytology, alpha fetoprotein (AFP) and beta human chorionic gonadotrophin (HCGbeta); a quantitative serum determination of AFP and HCGbeta should be performed at the time of the lumbar CSF assay Patient must have lumbar CSF for cytology, protein, AFP and HCGbeta within days prior to registration Subjects with histopathologic confirmation of intermediate or high-grade primary central nervous system lymphoma (PCNSL) as documented by brain biopsy, or cytology (analysis from cerebral spinal fluid [CSF] or vitrectomy), and cluster of differentiation (CD) positive; whenever possible, the tumor should be characterized by immunophenotype ELIGIBILITY CRITERIA - PHASE I (ARMS A, B, C): Patients must not have active central nervous system (CNS) leukemia, as defined by unequivocal morphologic evidence of lymphoblasts in the cerebrospinal fluid (CSF), use of CNS-directed local treatment for active disease within the prior days; previously treated CNS disease with documented cleared CSF will be allowed ELIGIBILITY CRITERIA - PHASE II (ARM D): Patients must not have active central nervous system (CNS) leukemia, as defined by unequivocal morphologic evidence of lymphoblasts in the cerebrospinal fluid (CSF), use of CNS-directed local treatment for active disease within the prior days; previously treated CNS disease with documented cleared CSF will be allowed Positive cerebrospinal fluid (CSF) cytology during staging, symptomatic leptomeningeal involvement, or parenchymal involvement of brain or spinal cord Positive cytology Patients with leptomeningeal metastases documented by MRI or cerebrospinal fluid (CSF) evaluation Lesions on imaging, by cerebrospinal fluid or with neurological findings that are consistent with leptomeningeal disease or meningeal carcinomatosis. Evidence of leptomeningeal disease on MRI or in cerebrospinal fluid (CSF) for arm ; ocular or mucosal disease specifically for patients with melanoma in arm Patients with leptomeningeal disease (leptomeningeal enhancement on MRI/CT imaging and/or positive cerebrospinal fluid [CSF] cytology) are not eligible to enroll Has evidence of leptomeningeal disease on MRI or in cerebrospinal fluid (CSF) Known active central nervous system metastases and/or lymphomatous meningitis; patients with isolated cerebrospinal fluid (CSF) involvement detectable by flow cytometry are eligible if clinically asymptomatic and if abnormal B cells are reported to be less than % by flow cytometry; subjects with previously treated central nervous system (CNS) disease may participate provided: ) any CNS-directed treatment was completed at least month prior to enrollment, ) imaging studies and CSF evaluation show no evidence of disease progression, and ) any neurologic symptoms have returned to baseline Patients requiring radiation for CNS diseases are excluded (CNS defined as brain soft tissue/intra parenchymal metastases within the gray and white matter of the brain and/or for cerebrospinal fluid [CSF] disseminated disease, including leptomeningeal carcinomatous disease) Patients with diffuse subependymal or cerebrospinal fluid (CSF) disease Patients with known brain, spinal or cerebrospinal fluid (CSF) involvement are excluded\r\n* Prophylactic intrathecal therapy is allowed per institutional protocol if deemed necessary Known central nervous system (CNS) leukemic involvement that is refractory to intrathecal chemotherapy and/or cranio-spinal radiation; patients with a history of CNS disease that have been effectively treated to complete remission (< white blood cell [WBC]/mm^ and no blasts in cerebrospinal fluid [CSF]) will be eligible. Known active DLBCL in the CNS (confirmed by cerebrospinal fluid [CSF] analysis). A history of AML related central nervous system (CNS) involvement is allowed if most recent cerebrospinal fluid (CSF) analysis is negative at least weeks prior to study treatment Subjects with detectable cerebrospinal fluid malignant cells or known brain metastases, or with a history of cerebrospinal fluid malignant cells or brain metastases. Subjects must not have known central nervous system involvement by disease (parenchymal, meningeal or cerebrospinal fluid) Has carcinomatous meningitis as determined by positive cerebrospinal fluid (CSF) cytology Active ALL in the central nervous system (CNS), as defined by >= leukocytes per microL with identifiable blast cells in the cerebrospinal fluid (CSF), and/or the presence of cranial-nerve palsies Evidence of cerebrospinal fluid (CSF) dissemination (positive CSF cytology for malignancy or MRI findings with CSF dissemination) Magnetic resonance (MR) imaging of the brain (performed within days of enrollment) must demonstrates no evidence of diffuse leptomeningeal spread beyond the primary relapse site in posterior fossa and no obstruction of cerebrospinal fluid flow (CSF) In patients with suspected leptomeningeal disease, the diagnosis of leptomeningeal disease should be confirmed by the presence of neurological or imaging signs and/or positive cerebrospinal fluid (CSF) cytology Absolute neutrophil count (ANC) >= /uL, without cerebrospinal fluid (CSF) support Patients with active or prior central nervous system (CNS) lymphoma or cerebrospinal fluid involvement with malignant lymphoma cells; NOTE: these patients are usually treated with CNS directed therapy; screening for cerebrospinal fluid (CSF)/CNS involvement is NOT required but can be performed per treating medical doctor (MD) discretion Diffuse subependymal or cerebrospinal fluid (CSF) disease Presence of active central nervous system (CNS) leukemia - cerebrospinal fluid (CSF) with < white blood count (WBC)/uL will not exclude the patient Active central nervous system (CNS) involvement by malignancy (patients with known positive cerebrospinal fluid [CSF] cytology or parenchymal lesions visible by computed tomography [CT] or magnetic resonance imaging [MRI]) RECIPIENT: Active central nervous system (CNS) involvement by malignancy (patients with known positive cerebrospinal fluid [CSF] cytology or parenchymal lesions visible by computed tomography [CT] or magnetic resonance imaging [MRI]) Active involvement of the central nervous system with malignancy; this can be documented as a normal neurological exam and/or a negative cerebrospinal fluid (CSF) analysis Patients will be excluded if there is radiographic or cerebrospinal fluid (CSF) cytological evidence of leptomeningeal disease Patients for who clinical suspicion is present of metastatic disease in the cerebrospinal fluid (CSF) or spine must have magnetic resonance imaging (MRI) of spine and CSF obtained (lumbar puncture or through Ommaya, external ventricular drain [EVD] or shunt) with negative cytology; patients with CSF that is positive for tumor cells or metastatic disease found on MRI are ineligible No evidence of metastatic disease in the brain, spine or cerebrospinal fluid (CSF); assessments must include magnetic resonance imaging (MRI) imaging of the brain and spine with and without contrast and a lumbar puncture for CSF cytology Lumbar cerebrospinal fluid (CSF) must be assayed for cytology, alpha fetoprotein (AFP) and beta human chorionic gonadotrophin (HCGB); a quantitative serum determination of AFP and HCGB should be performed at the time of the lumbar CSF assay Patient must have lumbar CSF for cytology, protein, AFP and HCGB within days prior to registration Active central nervous system (CNS) involvement by malignancy (patients with known positive cerebrospinal fluid [CSF] cytology or parenchymal lesions visible by computed tomography [CT] or magnetic resonance imaging [MRI]); except in the case of viral associated malignancies in which case the patient may benefit from the transplant to control the malignancy Active cerebrospinal fluid involvement with malignancy or brain metastasis Patients with MRI evidence of LMD, with or without evidence of malignant cells in CSF (positive cytology), or; patients with evidence of malignant cells in the CSF (positive cytology), with or without MRI evidence of LMD, or; patients with surgically-proven LMD (leptomeningeal involvement on pathology review) +/- MRI or CSF evidence by MRI or CSF cytology (Cohort D) Has active central nervous system (CNS) involvement (documented by radiologic lesions and/or malignant cells in the cerebrospinal fluid [CSF]). Patients are excluded if there is radiographic or cerebrospinal fluid (CSF) evidence of leptomeningeal disease. Patients must have histological verification of diagnosis. Patients with M+ disease (defined as evidence of neuraxis dissemination) are not eligible. Cerebrospinal fluid (CSF) cytology is not required but may be obtained if clinically indicated prior to study enrollment. If cytology is positive, the patient would be considered to have metastatic disease and would, therefore, be ineligible Lumbar CSF cytology is not required, but may be performed if clinically indicated prior to study enrollment. If lumbar CSF cytology is positive, the patient is considered to have M+ disease and is ineligible \r\n* Note: False positive cytology can occur within days of surgery Active or symptomatic central nervous system (CNS) disease\r\n* For study purposes, a subject will not be considered as having active CNS disease if the subject has documentation of prior CNS disease and has received prior treatment (IT or radiation) and is:\r\n** Asymptomatic for the last days prior to screening and\r\n** Has documented at least negative cerebrospinal fluid (CSF) cytology (which must include lumbar puncture [LP] within the study screening window) Evidence of cerebrospinal fluid (CSF) dissemination (positive CSF cytology for malignancy or MRI findings consistent with CSF dissemination). Active central nervous system (CNS) disease if a history of AML related CNS involvement, screening cerebrospinal fluid (CSF) analysis must be negative For stratum B, patients must have disseminated recurrent disease (defined as multifocal disease, positive spine MRI including leptomeningeal disease and/or positive cytology within days prior to study registration) and have adequate cerebrospinal fluid (CSF) flow based on spine MRI with no evidence of bulky disease or if bulky disease is present based on a CSF flow study per institutional guidelines; children must have undergone what is considered the standard of care as upfront therapy including either surgery followed by high dose chemotherapy with stem cell rescue or multi-modality therapy of surgery, radiation and chemotherapy Lumbar CSF must be obtained prior to study enrollment unless medically contraindicated; if a patient undergoes surgery and lumbar CSF cannot be obtained at this time, then it should be performed at least days following surgery before study enrollment; false positive cytology can occur within days of surgery; Note: patients with positive CSF cytology obtained prior to days after surgery may have cytology repeated to determine eligibility Patients with metastatic disease by cranial or spinal MRI evaluation or CSF cytology (unless medically contraindicated) are not eligible Relapsed/refractory primary vitreoretinal diffuse large B cell lymphoma (DLBCL) with a CNS lesion, with CSF relapse with positive CSF cytology, or with ocular relapse with positive ocular tissue biopsy; NOTE: tissue biopsy requirement of the CNS lesion is as outlined in bullet above Evidence of leptomeningeal disease by magnetic resonance imaging (MRI) and/or cerebrospinal fluid (CSF) cytology Lumbar cerebrospinal fluid (CSF) cytology examination must be obtained pre-operatively or within days following surgery; the optimal time for obtaining CSF is prior to surgery or - weeks following surgery; ventricular CSF (either pre- or post-op) may be used only if a post-operative spinal tap is contraindicated; if a spinal tap is contraindicated and there is no ventricular CSF available, then CSF cytology can be waived for patients with supratentorial tumors or if there is documentation of spinal subarachnoid metastases (M); patients who are categorized as M must have either an intra-operative positive CSF (via lumbar puncture at the end of the procedure) or a positive lumbar CSF obtained > days post-operatively High-risk medulloblastoma defined by any of the following:\r\n* > . cm^ residual disease for any medulloblastoma histology, or\r\n* Lumbar cerebral spinal fluid (CSF) cytology positive for tumor cells by analysis of fluid collected either before definitive surgery or at least days after definitive surgery unless contraindicated, or\r\n* Magnetic resonance imaging (MRI) evidence of M or M metastatic disease, or\r\n* M disease Active central nervous system (CNS) lymphoma, history of HIV-associated encephalopathy; dementia of any kind; seizures in the past months; patients with a history of positive cerebrospinal fluid cytology that has become negative with intrathecal chemotherapy and the patient has been in remission for at least months are eligible Patients with a history of central nervous system (CNS) leukemia must be stable, off steroids, with clear cerebrospinal fluid (CSF) for > months prior to day of Erwinaze administration (patient can receive monthly intrathecal maintenance chemotherapy) Highly suspicious magnetic resonance imaging (MRI) or cerebrospinal fluid (CSF) evidence of leptomeningeal metastases, unless all measurable disease is localized and SRS is considered the treatment of choice Patient must have negative lumbar cerebrospinal fluid (CSF) cytology (lumbar CSF must be obtained unless medically contraindicated); CSF cytology for staging should be performed preferably no sooner than days post operatively to avoid false positive CSF, ideally, CSF should be obtained between day and day to allow for final staging status before enrollment onto the study; Note: patients with positive CSF cytology obtained prior to days after surgery may have cytology repeated to determine eligibility and final CSF status Patients with metastatic disease by either MRI evaluation (brain and spine) or lumbar CSF cytology are not eligible Patients identified as needing spinal radiation at diagnosis (e.g. spinal metastasis or malignant cells identified on cerebrospinal fluid [CSF] cytology) are excluded Evidence of leptomeningeal disease by magnetic resonance imaging (MRI) and/or cerebrospinal fluid (CSF) cytology No known central nervous system (CNS) lymphoma or cerebrospinal fluid involvement with malignant lymphoma cells; these patients are usually treated with CNS directed therapy; screening for cerebrospinal fluid (CSF)/CNS involvement is NOT required but can be performed per treating medical doctor (MD) discretion; intrathecal (IT) methotrexate or IT cytarabine prophylaxis in patients with negative CSF who are felt to be at high risk of CNS relapse is allowed per local MD discretion; this should be noted on the treatment form STRATUM I:\r\n* Minimal disseminated disease (MDD) < % at diagnosis in T-lymphoblastic lymphoma (TLL)\r\n* No bone marrow involvement microscopically at diagnosis in B-lymphoblastic lymphoma \r\n* Patients should NOT have: \r\n** Any CNS involvement: CNS- status (i.e., >= white blood cell [WBC]/uL of cerebrospinal fluid [CSF] with blasts or cranial nerve palsy), CNS- status (< WBC/uL of CSF with blasts) or traumatic lumbar puncture (LP) (> red blood cell [RBC]/uL of CSF with blasts) \r\n** Overt testicular involvement (evidenced by ultrasonogram) For Primary Central Nervous System (CNS) Lymphoma (PCNSL): Subjects must have disease that is objectively measurable by International Workshop to Standardize Baseline Evaluation and Response Criteria in Primary CNS Lymphoma, Cerebrospinal Fluid (CSF) cytology (in case of leptomeningeal only disease), or vitreal aspiration cytology and/or retinal photographs (in case of ocular lymphoma). Recurrent/refractory CNS non-Hodgkin's lymphoma involving CNS (Brain, Cerebrospinal fluid (CSF) or intraocular compartments) Patients with central nervous system (CNS) leukemia are eligible as long as they have received treatment and most recent cerebrospinal fluid (CSF) analysis is negative for leukemia For patients with LM: Confirmed diagnosis of LM by positive CSF cytology. Have active leukemic central nervous system (CNS) involvement, as defined by any leukemic blasts detected in the cerebrospinal fluid (CSF) by morphology or flow cytometry and/or any chloromas detected by CNS imaging Patients may not have a known history of leptomeningeal disease, as diagnosed by positive cerebrospinal fluid (CSF) cytology, unless prospective permission for enrollment is granted from the sponsor and the PI Patients with parenchymal lesions must have unequivocal evidence of disease progression on imaging (MRI of the brain or head computed tomography [CT]) days prior to study registration; for patients with leptomeningeal disease only, CSF cytology must document lymphoma cells and/or imaging findings consistent with CSF disease days prior to study registration Diffuse subependymal or cerebral spinal fluid (CSF) disease Tumor involving both hemispheres or that which involves the subependyma or suspected cerebrospinal fluid dissemination Patients with active central nervous system (CNS) malignancy; asymptomatic small lesions are not considered active; treated lesions may be considered inactive if they are stable for at least months; patients with malignant cells in their cerebrospinal fluid (CSF) without CNS symptoms may be included Patient with solid tumor malignancy with leptomeningeal metastases established radiographically and/or through CSF cytology. Absolute neutrophil count (ANC) >= /uL, without cerebrospinal fluid (CSF) support Patients with infratentorial, multifocal, or pathologically confirmed cerebrospinal fluid (CSF) disseminated tumor Diagnosis of primary central nervous system (CNS) diffuse large B-cell lymphoma confirmed by one of the following:\r\n* Brain biopsy or resection\r\n* Cerebrospinal fluid\r\n* Vitreous fluid Known leptomeningeal or parenchymal brain involvement with lymphoma unless in complete remission after treatment for at least weeks with negative cerebrospinal fluid (CSF) cytology within weeks; prophylaxis of central nervous system (CNS) disease using intrathecal or intraventricular dosing of cytotoxic regimens is permitted and should be performed according to the discretion of the treating physician Active central nervous system (CNS) malignancy; however, patients with a history of positive Cerebrospinal fluid (CSF) cytology that has become negative with intrathecal chemotherapy are eligible. Evidence of diffuse leptomeningeal disease on brain MRI or by previously documented cerebrospinal fluid (CSF) cytology; NOTE: discrete dural metastases are permitted Participants must have histologically confirmed germ cell tumor or elevated alpha-fetoprotein (AFP) (serum > IU/L or cerebrospinal fluid [CSF] > than institutional norm) or beta-human chorionic gonadotropin (B-HCG) (serum or CSF > than institutional norm) in the setting of radiographic disease consistent with a germ cell tumor; disease must be confined to the central nervous system Patients with active brain metastases, or with a history of any central nervous system (CNS) metastases or cerebrospinal fluid malignant cells\r\n* Note: patients who are asymptomatic but are found to have malignant cells in the cerebrospinal fluid (CSF) on lumbar puncture prior to treatment will be considered eligible No evidence of CNS metastasis as indicated by MR images of the brain and spine and by cytologic examination of lumbar CSF to days after surgery; if lumbar puncture is medically contraindicated, ventricular CSF from a shunt or Ommaya reservoir may be used to rule out M disease; if CSF sampling is not possible and the patient has no other evidence of metastasis, the patient should be assigned to the intermediate risk arm No evidence of CNS metastasis as indicated by MR images of the brain and spine and by cytologic examination of lumbar CSF to days after surgery; if lumbar puncture is medically contraindicated, ventricular CSF from a shunt or Ommaya reservoir may be used to rule out M disease; if CSF sampling is not possible and the patient has no other evidence of metastasis, the patient will be assigned to the low risk arm Active central nervous system (CNS) involvement by malignancy (patients with known positive cerebrospinal fluid [CSF] cytology or parenchymal lesions visible by computed tomography [CT] or magnetic resonance imaging [MRI]) Patients must have a histologically confirmed diagnosis of a malignancy known to express GD; such tumors include medulloblastoma/primitive neuroectodermal tumor of the central nervous system (CNS), high grade astrocytomas, malignant glioma, neuroblastoma, retinoblastoma, ependymoma, rhabdoid tumors, sarcomas, melanoma or small cell lung carcinoma; for patients with other tumor types, GD expression must be confirmed by immunohistochemical staining and assessed by the Department of Pathology using prior frozen tissue, bone marrow or cerebrospinal fluid (CSF) cytology Patients with metastatic to CNS with only cerebral spinal fluid (CSF) involvement are NOT ELIGIBLE CSF cytology positive for malignant cells or symptomatic leptomeningeal carcinomatosis in the Phase b portion. In Group , subjects are required to have CSF cytology positive for malignant cells Cerebrospinal fluid (CSF) cytology for lymphoma or monoclonal lymphocyte population as defined by cell surface markers. CD+ B-cell primary central nervous system lymphoma (PCNSL) confirmed at the time of diagnosis by histology, cytology, or immunocytochemistry from cerebrospinal fluid (CSF); diagnosis must be documented by pathology report Subjects with detectable cerebrospinal fluid malignant cells, or brain metastases, or with a history of CNS lymphoma or primary CNS lymphoma, cerebrospinal fluid malignant cells or brain metastases Patients must have primary brain malignancy (histologically confirmed by surgical specimen or cerebral spinal fluid [CSF] cytology), or metastatic brain malignancy; if the patient has metastatic brain malignancy, there must be a histologic pathology report confirming the primary site of the cancer, as well as one of the following: confirmation by surgical specimen, CSF cytology, elevated tumor markers, or clinical evidence of CNS involvement Patients with active central nervous system (CNS) malignancy; asymptomatic small lesions are not considered active; treated lesions may be considered inactive if they are stable for at least months; patients with malignant cells in their cerebrospinal fluid (CSF) without CNS symptoms may be included Patients with active CNS malignancy. Asymptomatic small lesions are not considered active. Treated lesions may be considered inactive if they are stable for at least months. Patient with malignant cells in their cerebrospinal fluid (CSF) without CNS symptom may be included. Evidence of leptomeningeal disease by MRI and/or cerebrospinal fluid (CSF) cytology History of seizures, elevated intracranial pressure (ICP) or cerebrospinal fluid (CSF) obstructive states (e.g. severe head injury, central congenital or mass lesions) Patients who are not a candidate for intrathecal drug therapy due to coagulopathy, concurrent necessary use of blood thinners, presence of systemic infection, drug allergy to analgesic agent, evidence of cerebrospinal fluid (CSF) obstruction or other technical factor Patients with parenchymal lesions must have unequivocal evidence of disease progression on imaging (MRI of the brain or head computed tomography [CT]) days prior to study registration; for patients with leptomeningeal disease only, CSF cytology must document lymphoma cells and/or imaging findings consistent with CSF disease days prior to study registration (at the discretion of the investigator) For medulloblastoma patients only, positive CSF cytology Subjects with active CNS or cerebrospinal fluid (CSF) involvement by malignancy Immunocompetent patients with newly diagnosed or recurrent non-Hodgkins lymphoma involving the brain (primary or secondary), as demonstrated by magnetic resonance imaging (MRI) and histologic confirmation either by positive cerebrospinal fluid (CSF) cytology for lymphoma or a monoclonal lymphocyte population defined by cell surface markers, vitreous or uvea biopsy or brain biopsy Participants with glioblastoma involving the brainstem or posterior fossa, cerebrospinal fluid dissemination Presence of radiographically suspected leptomeningeal disease (LM) or carcinomatous meningitis (CM) AND/OR presence of at least one CNS lesion for which the following criteria are met:\r\n* For patients without leptomeningeal disease: presence of at least one parenchymal CNS lesion that is at least mm in size; Note: intra-cranial disease assessments can only be performed using contrast-enhanced magnetic resonance imaging (MRI); MRI scan slices of mm are necessary for brain metastases between and mm in size\r\n* The lesion(s) must be newly diagnosed or be present as progression after local therapy, including surgery and/or radiation therapy; for patients who have received local therapy, progression of pre-existing lesions based on RECIST v. (> % increase in longest diameter on baseline scan) or new lesions are required\r\n* Participants who are receiving corticosteroids must be on a stable or decreasing dose for at least week prior to the first dose of study treatment\r\n* For patients with suspected LM or CM based on imaging, spinal fluid sampling for confirmation is not required; for patients who do undergo spinal fluid sampling, those with negative spinal fluid (CSF) are eligible to enter Subjects with detectable cerebrospinal fluid malignant cells or brain metastases or with a history of cerebrospinal fluid malignant cells or brain metastases