Novel Combinations of CC-122, CC-223, CC-292, and Rituximab in Diffuse Large B-cell Lymphoma and Follicular Lymphoma

Inclusion Criteria: * Men and women, 18 years or older, with histologically or cytologically-confirmed either: 1. Chemo-refractory DLBCL (including transformed low grade lymphoma) 2. Lenalidomide naïve; relapsed or refractory CD20-positive follicular lymphoma (Grade 1, 2, or 3a) following at least one prior standard systemic treatment regimen including systemic chemo-, immune-; or chemo-immunotherapy and at least one prior line of salvage therapy with no prior exposure to lenalidomide, or double-refractory FL participants with no prior exposure to lenalidomide (FL-1 cohort) 3. Lenalidomide exposed: relapsed or refractory CD20-positive follicular lymphoma (Grade 1, 2, or 3a) previously treated with at least two cycles of lenalidomide-containing regimen (FL-2 cohort), either as a single agent or in combination * At least one site of measurable disease * Eastern Cooperative Oncology Group (ECOG) Performance Status (PS) of 0 or 1. * Participants must have the following laboratory values: * Absolute Neutrophil Count (ANC) ≥ 1.5 x 109/L or ≥ 1.0 x 109/L (with bone marrow involvement with DLBCL) * Hemoglobin (Hgb) ≥ 8 g/dL. * Potassium within normal limits * Asparate Aminotransferase/Serum Glutamic Oxaloacetic Transaminase (AST/SGOT) and Alanine Aminotransferase/Serum Glutamic-Pyruvic Transaminase (ALT/SGPT) ≤ 2.5 x Upper Limit of Normal (ULN) or ≤ 5.0 X ULN if liver tumor is present. * Serum bilirubin ≤ 1.5 x ULN. * Estimated serum creatinine clearance of ≥ 50 mL/min * Participants must have the following laboratory values: Absolute Neutrophil Count (ANC) ≥ 1.5 x 109/L without growth factor support for 7 days (14 days if participants received pegfilgrastim). * Males enrolled into treatment arms receiving CC-122 must: Agree to abstain from donating sperm while taking IP and for at least 95 days following discontinuation of IP Exclusion Criteria: * Symptomatic central nervous system involvement. * Known symptomatic acute or chronic pancreatitis. * Persistent diarrhea or malabsorption despite medical management. * Peripheral neuropathy ≥ grade 2 * Impaired cardiac function or clinically significant cardiac diseases * Participants with diabetes on active treatment (for participants treated on CC-223 containing arms only) * Prior autologous stem cell transplant (ASCT) ≤ 3 months before first dose. * Prior allogeneic stem cell transplant with either standard or reduced intensity conditioning. * Prior systemic cancer-directed treatments or investigational modalities ≤ 5 half lives or 4 weeks prior to starting study drugs, whichever is shorter. * Participants who have undergone major surgery ≤ 2 weeks prior to starting study drugs. * Women who are pregnant or breast feeding. Adults of reproductive potential not willing to employ two forms of birth control. * Participants with known HIV infection, chronic active hepatitis B or C virus (HBV/HCV) infection. * Participants with treatment-related myelodysplastic syndrome. * History of concurrent second cancers requiring active, ongoing systemic treatment. * Prior treatment with a dual mTORC1/mTORC2 inhibitor (CC-223 arms only) or BTK inhibitor (PCI-32765) (CC-292 arms only). \[Prior treatment with rapamycin analogues, PI3K or AKT inhibitors, lenalidomide and rituximab are allowed\].