Previous treatment with brentuximab vedotin will be allowed if it was done 6 months prior to enrollment and was not refractory to or had progressive disease (PD) on brentuximab vedotin (BV)Xx_NEWLINE_xXPregnancy or breast-feeding women; breastfeeding should be discontinued if the mother is treated with brentuximab vedotinXx_NEWLINE_xXFor patients with CD30+ ALCL, failed or are ineligible or intolerant to brentuximab vedotinXx_NEWLINE_xXBrentuximab vedotin naive OR had at least stable disease by Lugano Classification to prior brentuximab vedotin treatmentXx_NEWLINE_xXRefractory to prior brentuximab vedotin (i.e. progression while on treatment)Xx_NEWLINE_xXHistory of prior >= grade 3 hypersensitivity to either brentuximab vedotin or nivolumabXx_NEWLINE_xXBrentuximab vedotinXx_NEWLINE_xXPrior treatment with at least 2 lines of therapy for HL including brentuximab vedotin; in those patients who cannot receive brentuximab vedotin, treatment with 2 prior therapeutic regimens is sufficientXx_NEWLINE_xXPrior treatment with brentuximab vedotin is allowed provided the patient did not progress on BV or within 30 days of last dose of BV; patients must be at least 3 months from the last dose of BVXx_NEWLINE_xXRefractory to prior therapy with brentuximab vedotin (evidence of progression within 30 days of the last dose)Xx_NEWLINE_xXPrevious exposure to brentuximab vedotin (BV)Xx_NEWLINE_xXPrior brentuximab vedotin is allowed in the dose-finding portion of the study (dose-finding cohort); in the expansion cohort, patients cannot be refractory to BV (defined as developing progressive disease while on treatment or progressed within 3 months of finished last dose of brentuximab vedotin)Xx_NEWLINE_xXFailed >= 2 prior systemic therapies\r\n* NOTE: For systemic anaplastic large cell lymphoma (ALCL) prior systemic therapy must also include progression on brentuximab vedotinXx_NEWLINE_xXKnown hypersensitivity to brentuximab vedotin componentsXx_NEWLINE_xXHistologically confirmed CD30-positive (defined in this study as >= 1% expression) MF (including large cell transformation variant) or SS who have either:\r\n* Received prior systemic therapy (for whom commercial supply of brentuximab vedotin is available) OR\r\n* Not received prior systemic therapy (who will receive brentuximab vedotin free of charge)Xx_NEWLINE_xXPrevious brentuximab treatmentXx_NEWLINE_xXPrior brentuximab vedotin is allowed provided that patients were not refractory (defined as developing progressive disease while on treatment or progressed within 3 months of finished last dose of brentuximab vedotin)Xx_NEWLINE_xXPatient has hypersensitivity to brentuximab vedotinXx_NEWLINE_xXRefractory to prior brentuximab vedotin (defined as developing progressive disease while on treatment or progressed within 3 month of finished last dose of brentuximab vedotin)Xx_NEWLINE_xXPatients who have received prior histone deacetylase (HDAC) inhibitors, or brentuximab vedotin, may be permitted to enter the study unless they have received an HDAC inhibitor or brentuximab within the last 6 monthsXx_NEWLINE_xXEligible to receive standard brentuximab vedotin for relapsed Hodgkin lymphomaXx_NEWLINE_xXPatients with prior receipt of brentuximab vedotinXx_NEWLINE_xXPatients may have received prior brentuximab vedotin, but must not have received brentuximab vedotin within 6 months prior to registration, and must not have relapsed within 6 months of receiving previous brentuximab vedotin; patients may not have received prior nivolumab or PD1/PDL1 axis agents; patients in the nivolumab/brentuximab cohorts ONLY (D, E, F, Y) may have received prior ipilimumabXx_NEWLINE_xXPatients must not have previously existing hypersensitivity to brentuximab vedotin or ipilimumabXx_NEWLINE_xXRANDOMIZED PHASE II (ARMS K AND L): Patients may have received prior brentuximab vedotin, but must not have received brentuximab vedotin within 6 months prior to registration, and must not have relapsed within 6 months of receiving previous brentuximab vedotin; patients may not have received prior nivolumab or PD1/PDL1 axis agents; patients may not have received prior ipilimumabXx_NEWLINE_xXRANDOMIZED PHASE II (ARMS K AND L): Patients must not have previously existing hypersensitivity to brentuximab vedotin or ipilimumabXx_NEWLINE_xXRelapsed or refractory CD30+ lymphoma that has either achieved < PR to brentuximab vedotin (minimum of 2 cycles), progressed while receiving brentuximab vedotin, or progressed within 6 months of the last dose of brentuximab vedotinXx_NEWLINE_xXResolution of all non-hematologic brentuximab vedotin-related adverse events (AEs) to < grade 2Xx_NEWLINE_xXIntolerance to brentuximab vedotinXx_NEWLINE_xXPatients receiving chronic treatment with systemic steroids; however, patients can receive up to 10 days of steroid therapy prior to starting treatment with brentuximab vedotin (BV)+ doxorubicin, vinblastine, dacarbazine (AVD)Xx_NEWLINE_xXMay have received either brentuximab vedotin or lenalidomide/immunomodulatory imide drugs (IMiD) without dose modification/delay due to toxicity\r\n* IMiDs defined as thalidomide analoguesXx_NEWLINE_xXIf received prior brentuximab vedotin or lenalidomide, must be able to tolerate the dose level to which the participant will be enrolled toXx_NEWLINE_xXAllergic reaction/hypersensitivity to lenalidomide or history of anaphylactic shock to brentuximab vedotin in the pastXx_NEWLINE_xXPreviously untreated with either chemotherapy, radiation therapy or either brentuximab vedotin or nivolumab, or another check point inhibitorXx_NEWLINE_xXAllergy to brentuximab vedotin and/or nivolumabXx_NEWLINE_xXPrior treatment with brentuximab vedotin (BV)Xx_NEWLINE_xXKnown allergy to bevacizumab or brentuximab vedotin or any of its excipientsXx_NEWLINE_xXRelapsed or refractory disease after standard therapy including brentuximab vedotin (Adcetris®).Xx_NEWLINE_xXPreviously treated with brentuximab vedotin, immune-oncology agents, or received an allogeneic or autologous stem cell transplantXx_NEWLINE_xXClassical Hodgkin lymphoma\r\n* Relapsed or refractory de novo classical Hodgkin lymphoma having failed standard first-line therapy; and\r\n* May have failed to achieve a response or progressed after treatment with brentuximab vedotin or may be brentuximab vedotin naïve but is ineligible or unable to receive brentuximab vedotin; and\r\n* May have failed to achieve a response to, progressed after, or is ineligible for autologous stem cell transplant (auto-SCT)Xx_NEWLINE_xXSubjects may be Brentuximab vedotin- naïve, or may have had prior Brentuximab vedotin treatment (cohort A, B & C - enrolment closed)Xx_NEWLINE_xXPrior treatment with brentuximab vedotin is allowed provided the patient did not progress on BV or within 30 days of last dose of BV; patients must be at least 3 months from the last dose of BVXx_NEWLINE_xXKnown to have active hepatitis C infection (positive by polymerase chain reaction) or on antiviral therapy for hepatitis C within 6 months prior to the first doses of brentuximab vedotin and lenalidomideXx_NEWLINE_xXKnown hypersensitivity to any excipient contained in the drug formulation of brentuximab vedotin or lenalidomideXx_NEWLINE_xXRefractory to prior therapy with brentuximab vedotin (evidence of progression within 30 days of the last dose)Xx_NEWLINE_xXFemale patients of childbearing age must have negative urine or serum pregnancy test; subjects agree to use an acceptable method for contraception during the entire study treatment period and through 6 months after the last dose of brentuximab vedotinXx_NEWLINE_xXMale subject agrees to use an acceptable method for contraception during the entire study treatment period and through 6 months after the last dose of brentuximab vedotinXx_NEWLINE_xXPrevious primary progression or grade 3 toxicity on treatment with brentuximab vedotinXx_NEWLINE_xXParticipant may have failed to achieve a response or progressed after treatment with brentuximab vedotin or may be brentuximab vedotin naïveXx_NEWLINE_xXIf female of childbearing age, negative serum pregnancy test within 7 days prior to the first dose of brentuximab vedotin in this studyXx_NEWLINE_xXPrior treatment with brentuximab vedotin and bendamustine in combination; may have received prior therapy with brentuximab vedotin or bendamustine separatelyXx_NEWLINE_xXReceived either brentuximab vedotin or bendamustine within 3 months of receiving their first dose of protocol based therapyXx_NEWLINE_xXIf brentuximab vedotin or bendamustine was previously received, had disease progression during the first 3 cycles of either brentuximab vedotin or bendamustineXx_NEWLINE_xXKnown hypersensitivity to brentuximab vedotin, bendamustine, or mannitolXx_NEWLINE_xXKnown hypersensitivity to any excipient contained in the drug formulation of brentuximab vedotin or any component of ABVDXx_NEWLINE_xXPrior to day 1 of brentuximab vedotin, please verify the patient does not meet the criteria below:\r\n* Symptomatic pulmonary disease currently requiring regular medication including but not restricted to bronchodilatorsXx_NEWLINE_xXPrevious receipt of brentuximab vedotin Please note that there are additional inclusion and exclusion criteria. The study center will determine if you meet all of the criteria.Xx_NEWLINE_xXPatients must have received at least 2 prior regimens and have received or be deemed ineligible for autologous stem cell transplant, and must have received prior brentuximab vedotinXx_NEWLINE_xXPrevious treatment with brentuximab vedotinXx_NEWLINE_xXPrior use of brentuximab vedotinXx_NEWLINE_xXPatients with previous exposure to brentuximab pre-transplant are eligible for the studyXx_NEWLINE_xXMust have had prior treatment with brentuximab vedotin or not a candidate for treatment with brentuximab vedotinXx_NEWLINE_xXPrior administration of brentuximab vedotinXx_NEWLINE_xXPrevious treatment with brentuximab vedotin or bendamustine.Xx_NEWLINE_xXKnown hypersensitivity to any excipient contained in the drug formulation of brentuximab vedotinXx_NEWLINE_xXNo prior brentuximab vedotinXx_NEWLINE_xXPatient has hypersensitivity to brentuximab vedotinXx_NEWLINE_xXPatient has received other investigational drugs within 14 days before treatment of treatment with brentuximab vedotinXx_NEWLINE_xXIn addition to the inclusion/exclusion criteria outlined, to be eligible for treatment with the higher 2.4 mg/kg dose of brentuximab vedotin in the new cohort of 20 additional patients, best response after 2 cycles of brentuximab vedotin administered at the 1.8 mg/kg dose, must be partial remission (PR) or stable disease (SD) as determined by radiographic imagingXx_NEWLINE_xXViral, bacterial, or fungal infection within two weeks prior to the first dose of brentuximab vedotinXx_NEWLINE_xXPrevious treatment with brentuximab vedotin.Xx_NEWLINE_xXPrior use of brentuximab vedotin for GVHD is not allowed; prior use of brentuximab vedotin for the treatment of malignancy is allowedXx_NEWLINE_xXPatient must not have had prior exposure to brentuximab vedotinXx_NEWLINE_xXPrior use of brentuximab vedotin for GVHD is not allowed; prior use of brentuximab vedotin for the treatment of malignancy, i.e. Hodgkin lymphoma, anaplastic large cell lymphoma, etc. is allowedXx_NEWLINE_xX