Histologically or cytologically confirmed small cell lung cancer Patients must be newly diagnosed with histologically confirmed intracranial ependymoma; patients with classic ependymoma (WHO II) or anaplastic ependymoma (WHO III) are eligible, as are various subtypes described as clear cell, papillary, cellular or a combination of the above Patients must have histologically confirmed relapsed or refractory mantle cell lymphoma or low grade B-cell non-Hodgkin lymphoma (NHL); patients with evidence of transformation to a high grade histology will not be eligible Pathologically (histologically or cytologically) proven diagnosis of invasive breast cancer Histologically or cytologically confirmed, newly diagnosed non-squamous NSCLC Histologically or cytologically confirmed hematologic malignancy Patients must have histologically confirmed, newly diagnosed or recurrent from a previously treated early stage lung cancers that are locally confined, non-small cell lung cancers that are considered unresectable and for which chemoradiation will be considered definitive therapy; patients with recurrent cancer that is amendable for chemoradiation can be eligible only if patients with prior lobectomy for stage I cancer had not had adjuvant chemotherapy, and more than 8 weeks have elapsed from surgery to allow for wound healing; patients who recur from prior X-ray therapy (XRT) or stereotactic body radiation therapy (SBRT) will not be eligible Study participants must have histologically or cytologically confirmed unresectable or metastatic malignant melanoma Histologically or cytologically proven diagnosis of non-small cell lung cancer Patients must have histologically or cytologically diagnosed advanced anaplastic thyroid cancer (ATC) Patients must have histologically or cytologically confirmed primary central nervous system diffuse large B-cell lymphoma; only patients with relapsed or refractory disease are eligible; patients with PCNSL that is only extracranial will not be eligible In dose escalation, patients must have histologically or cytologically confirmed metastatic disease from any solid tumor; in dose expansion, patients must have histologically or cytologically confirmed metastatic melanoma, renal cell carcinoma, ovarian cancer, or colorectal cancer Patients must have histologically or cytologically confirmed stage IV (American Joint Committee on Cancer [AJCC] 7th Edition) or recurrent non-small cell lung cancer (NSCLC) Arm A dose escalation: patients with histologically or cytologically proven advanced solid tumors for which standard treatments are not available, or for whom the current dose level of cisplatin in combination with pemetrexed is appropriate; =< 2 prior cytotoxic chemotherapy regimen Arm A dose level 4 (75 mg/m^2 cisplatin): patients with histologically proven chemotherapy-naive advanced unresectable solid tumors for which pemetrexed combined with cisplatin is an indicated regimen (malignant mesothelioma, non-small cell lung cancer, ovarian cancer and thymoma) Arm A 14-patients expansion cohort: patients with histologically or cytologically proven chemotherapy naive unresectable malignant pleural or peritoneal mesothelioma Stratum D: Patients must have a histologically confirmed diagnosis of ependymoma that is recurrent, progressive or refractory following therapy which included radiotherapy Stratum E: Patients must have a histologically confirmed diagnosis of medulloblastoma that is recurrent, progressive or refractory following therapy which included radiotherapy Patients must have histologically or cytologically confirmed stage IV or recurrent squamous cell lung cancer that harbors any of the NFE2L2 mutations; any KEAP1 mutation will be eligible Patients must have pathologically/histologically confirmed tumor of non-small cell histology Patients with stage IV or recurrent/metastatic histologically confirmed non-small cell lung cancer (NSCLC) Patients with stage IV or recurrent/metastatic histologically or cytologically confirmed non-squamous NSCLC Histologically or cytologically confirmed relapsed cluster of differentiation (CD)19+ non-Hodgkin lymphoma (NHL) (included in this category are follicular grade I, II, III, marginal zone, mantle cell, gray zone, primary mediastinal, Burkitt's, diffuse large B cell, small lymphocytic lymphoma) Patients must have histologically or cytologically confirmed metastatic urothelial carcinoma; urothelial cancer derived from the bladder, ureter or upper tract is permitted Patients with a histologically confirmed diagnosis of non-small cell lung cancer (NSCLC), including neuroendocrine tumors or small cell lung cancer (SCLC) who are being evaluated for palliative WBRT (with or without neurosurgical resection or stereotactic radiosurgery [SRS]) for radiologically or histologically diagnosed brain metastases presumed to be from the lung cancer are eligible for this Phase I study; group 2 will only include NSCLC patients Patients must have histologically or cytologically confirmed clear cell renal cell carcinoma (RCC) COHORT B: Patients must have histologically or cytologically confirmed primary desmoplastic melanoma that is unresectable; patients in Cohort B must have measurable disease per RECIST 1.1 Patients must have histologically or cytologically confirmed non-small cell lung cancer (cohort 1) or colorectal cancer (cohort 2) Histologically or cytologically confirmed diagnosis of extensive-stage small cell lung cancer with no prior systemic treatment Pathologically (histologically or cytologically) or radiographically-proven (based on the American Association for the Study of Liver Diseases [AALSD] criteria) unresectable or locally recurrent hepatocellular cancer prior to registration