Inclusion Criteria:
All Cohorts:
* Life expectancy of \>= 3 months on standard of care (SOC).
* Must have an Eastern Cooperative Oncology Group (ECOG) performance status score 0 - 2.
* Has one or more measurable disease sites:
* Fluorodeoxyglucose-positron emission tomography (FDGPET) scan demonstrating positive lesion compatible with computed tomography (CT) or magnetic resonance image (MRI)-defined anatomical tumor sites.
* \>= 1 measurable nodal lesion (long axis \> 1.5 cm and short axis \> 1.0 cm) or \>= 1.0 measurable extra-nodal lesion (long axis \>= 1 cm) on CT scan or MRI. Note: A previously irradiated lesion must have demonstrated progression or residual disease in the lesion after radiotherapy to be considered measurable.
Cohort 1 Part 1 (Monotherapy Safety Run-in) Specific Criteria:
* Must have histologically confirmed CD20+ Diffuse large B-cell lymphoma (DLBCL), or High-grade B-cell lymphoma (HGCBL) with MYC and BCL2 and/or BCL6 translocations and DLBCL feature, and follicular Lymphoma (FL) at most recent (previous or current) representative tumor biopsy based on the pathology report, according to the World Health Organization (WHO) 2016 (or later) classification.
* Must have at least one prior treatment with an anti-CD20 monoclonal antibody (e.g., rituximab) potentially in combination with chemotherapy and/or relapsed after autologous stem cell rescue.
* Must have relapsed or refractory disease. Note: Relapsed disease is defined as disease that has recurred \>= 6 months after completion of therapy. Refractory disease is defined as disease that either progressed or failed to achieve an objective response during therapy or progressed within 6 months (\<6 months) of completion of therapy.
Cohort 1 Part 2 (Monotherapy Expansion) Specific Criteria:
* Must have histologically confirmed CD20+ DLBCL at most recent (previous or current) representative tumor biopsy based on the pathology report, inclusive of the following according to the World Health Organization (WHO) 2016 (or later) classification.
* DLBCL, not otherwise specified (NOS) including de novo or histologically transformed from an earlier diagnosis of indolent lymphoma such as FL and nodal marginal zone lymphoma with a subsequent development of DLBCL relapse or.
* "Double-hit" or "triple-hit" with DLBCL morphology (technically classified in WHO 2016 as HGBCL, with MYC and BCL2 and/or BCL6 translocations). Note: Double- /triple-hit lymphomas without DLBCL morphology and those classified in WHO 2016 as HGBCL, NOS are not eligible.
* FL Grade 3B.
* Following safety run-in and up to the 12th participant (including the number of safety run-in participants) in Cohort 1, participants must have received at least 1 prior line of systemic therapies which must include an anti-CD20 monoclonal antibody containing combination therapy (e.g., rituximab). After safety run-in confirms tolerability of the full dose A of epcoritamab, participants must have received at least 2 prior lines of systemic therapies.
* Must have either failed prior autologous HSCT, or be ineligible for autologous HSCT due to age, comorbidities, performance status, comorbidities, or insufficient response to prior treatment.
* Must have relapsed or refractory disease. Note: Relapsed disease is defined as disease that has recurred \>= 6 months after completion of therapy. Refractory disease is defined as disease that either progressed or failed to achieve an objective response during therapy or progressed within 6 months (\< 6 months) of completion of therapy.
Cohort 2 Specific Criteria:
* Must have newly diagnosed CD20+ DLBCL.
* Must have one of the following histologically confirmed CD20+ DLBCL (de novo or histologically transformed from FL at most recent (previous or current) representative tumor biopsy based on the pathology report including one of the following diagnoses according to the WHO 2016 (or later) classification:
* DLBCL, not otherwise specified (NOS);
* "Double-hit" or "triple-hit" with DLBCL morphology (technically classified in WHO 2016 as HGBCL, with MYC and BCL2 and/or BCL6 translocations) Note: Double-/triple-hit lymphomas without DLBCL morphology and those classified in WHO 2016 as HGBCL, NOS are not eligible or;
* FL Grade 3B
* Eligible for standard R-CHOP for 6 cycles.
Cohort 3 Specific Criteria:
* Must have histologically confirmed CD20+ Grade 1 - 3a Follicular Lymphoma stage II, III, or IV with no evidence of histologic transformation to an aggressive lymphoma at most recent (previous or current) representative tumor biopsy and based on the pathology report, according to the WHO 2016 (or later) classification.
* Must have R/R disease to at least one prior systemic anti-lymphoma treatment which must include an anti CD20 monoclonal antibody (e.g., rituximab). Participant who received only prior anti-CD20 monoclonal antibody monotherapy is not eligible. Note: Relapsed disease is defined as disease that previously responded to therapy but progressed \>= 6 months after completion of therapy. Refractory disease is defined as disease that either progressed during therapy, failed to achieve an objective response or progressed within 6 months (\< 6 months) of completion of therapy.
* Must be eligible for R2 per investigator determination.
* Willing to take aspirin prophylaxis (participants with low or intermediate risk for thromboembolism) or prophylactic anticoagulant (if high risk for a thromboembolic event) (lenalidomide treated participants only).
Exclusion Criteria:
All Cohorts:
* History of primary mediastinal lymphoma.
* Autologous Stem Cell Transplantation within 100 days prior to enrollment.
* Have received prior allogeneic hematopoietic stem cell transplantation at any time.
* Have been treated with a bispecific antibody targeting CD3 and CD20.
Cohort 2 Specific Criteria:
\- History of prior systemic anti-lymphoma therapy (including definitive radiotherapy) for Diffuse large B-cell lymphoma (DLBCL) other than corticosteroids.
