Pts must agree to take enteric-coated aspirin mg orally daily, or if history of prior thrombotic disease, must be fully anticoagulated with warfarin (INR -) or be treated with full-dose, low molecular weight heparin, as if to treat deep venous thrombosis (DVT)/pulmonary embolism (PE)at the investigator's discretion Requirement of therapeutic anticoagulant therapy with oral vitamin K antagonists; low-dose anticoagulants for maintenance of patency of central venous access devise or prevention of deep venous thrombosis is allowed; therapeutic use of low molecular weight heparin (or similar parenteral drug) for venous-thromboembolic disease is allowed Requirement of anticoagulant therapy with oral vitamin K antagonists such as Coumadin (warfarin). Low-dose anticoagulants for the maintenance of patency in a central venous access device or the prevention of deep vein thrombosis or pulmonary embolism is allowed. Therapeutic use of low molecular weight heparin is allowed provided patients are safely able to interrupt it prior to biopsy procedures. If prior history of deep vein thrombosis (DVT)/pulmonary embolism (PE), the patient needs to be on stable doses of anticoagulation with low molecular weight heparin or oral anticoagulant for at least two weeks Deep venous thrombosis within months prior to study treatment, unless the patient is anti-coagulated without the use of warfarin for ? weeks prior to study treatment; in this situation, low molecular weight heparin is preferred Recent occurrence (within to months) of a major thromboembolic event, such as pulmonary embolism or proximal deep vein thrombosis, unless stable on (> month) therapeutic anticoagulation (aspirin < milligrams (mg) daily or low-molecular-weight heparin [LMWH]). Participants with a history of clinically non-significant thromboembolic events, not requiring anticoagulation, are allowed on study. Requirement of anticoagulant therapy with oral vitamin K antagonists such as Coumadin (warfarin); low-dose anticoagulants for the maintenance of patency in a central venous access device or the prevention of deep vein thrombosis or pulmonary embolism is allowed; therapeutic use of low molecular weight heparin is allowed Deep vein thrombosis (DVT) or pulmonary embolus which require use of oral anticoagulants or, if on low molecular weight heparin, have not been on a stable dose for at least weeks Participants must agree to ongoing anticoagulation as prophylaxis against deep vein thrombosis (DVT) using aspirin ( or mg) daily, warfarin or low molecular weight heparin, or a patient already taking another oral anticoagulant (e.g. direct thrombin inhibitors for atrial fibrillation) may continue that agent Has had a symptomatic venous thrombosis within weeks prior to study enrollment - NOTE: Subjects with a history of a deep vein thrombosis > weeks prior to study enrollment who are on anticoagulation therapy with low molecular weight heparin are eligible for this study Recent venous thrombosis within weeks prior to study registration; patients at high risk for thrombotic events due to inherited risk factors (i.e. factor V Leiden) or deep vein thrombosis (DVT)/pulmonary embolism (PE) in the past months should be on secondary prophylaxis with anti-coagulant therapy (i.e. warfarin or low molecular weight heparin) prior to enrollment Patients may have a history of current or previous deep vein thrombosis or pulmonary embolism but must be willing to initiate prophylaxis with low molecular weight heparin Patients being treated with full dose warfarin are excluded. Patients with history of deep vein thrombosis or pulmonary embolus who are being treated with therapeutic doses of low molecular weight heparin or prophylactic dose anticoagulants may be enrolled. Patients must agree to take enteric coated aspirin mg orally daily, or if history of prior thrombotic disease, must be fully anticoagulated with warfarin (international normalized ratio [INR] -) or be treated with full dose, low molecular weight heparin, as if to treat deep venous thrombosis (DVT)/pulmonary embolism (PE) Has had a symptomatic venous thrombosis within the days prior to study enrollment - NOTE: Subjects with a history of a deep vein thrombosis days prior to study enrollment who are on anticoagulation therapy with low molecular weight heparin are eligible for this study Angina, MI, symptomatic congestive heart failure, cerebrovascular accident, transient ischemic attack, arterial embolism, pulmonary embolism, PTCA or CABG within the past months. Deep venous thrombosis within months, unless the patient is anti-coagulated without the use of warfarin for at least weeks. In this situation, low molecular weight heparin is preferred. Absence of history of deep venous thrombosis/embolism, threatening thromboembolism or known thrombophilia; patients with a history of deep vein thrombosis(DVT)/pulmonary embolism (PE) or thrombophilia may participate if they are willing to be on full anticoagulation during the treatment if randomized to rituximab, cyclophosphamide, doxorubicin hydrochloride, vincristine sulfate, and prednisone (RCHOP) arm A; full anticoagulation is defined as warfarin, factor X inhibitors, or low molecular weight heparin at therapeutic doses Has had a deep venous thrombosis (DVT) or pulmonary embolism within the months prior to study enrollment. NOTE: Subjects with a history of a DVT or pulmonary embolism > months prior to study enrollment who are on anticoagulation therapy with low molecular weight heparin are eligible for this study. Angina, MI, symptomatic congestive heart failure, cerebrovascular accident, transient ischemic attack, arterial embolism, pulmonary embolism, PTCA or CABG within the past months. Deep venous thrombosis within months unless the patient is anticoagulated without the use of warfarin for at least weeks. In this situation, low molecular weight heparin is preferred. Patients must have no medical contra-indications to, and be willing to take, deep vein thrombosis (DVT) prophylaxis as all patients registering to the lenalidomide/rituximab Arms G and H will be required to have deep vein thrombosis (DVT) prophylaxis; patients randomized to Arms G or H who have a history of a thrombotic vascular event will be required to have full anticoagulation, therapeutic doses of low-molecular weight heparin or warfarin to maintain an international normalized ratio (INR) between .-., or any other accepted full anticoagulation regimen (e.g., direct thrombin inhibitors or factor Xa inhibitors) with appropriate monitoring for that agent; patients on Arms G and H without a history of a thromboembolic event are required to take a daily aspirin ( mg or mg) for DVT prophylaxis; patients who are unable to tolerate aspirin should receive low molecular weight heparin therapy or warfarin treatment or another accepted full anticoagulation regimen Patients must have no medical contra-indications to, and be willing to take, DVT prophylaxis as all patients registering to the lenalidomide/rituximab Arms G and H will be required to have deep vein thrombosis (DVT) prophylaxis; patients randomized to Arms G or H who have full anticoagulation, a history of a thrombotic vascular event will be required to have therapeutic doses of low molecular weight heparin or warfarin to maintain an INR between . ., or any other accepted full anticoagulation regimen (e.g., direct thrombin inhibitors or factor Xa inhibitors) with appropriate monitoring for that agent; patients on Arms G and H without a history of a thromboembolic event are required to take a daily aspirin ( mg or mg) for DVT prophylaxis; patients who are unable to tolerate aspirin should receive low molecular weight heparin therapy or warfarin treatment or another accepted full anticoagulation regimen Patients with known tumor thrombus or deep vein thrombosis are eligible if stable on low molecular weight heparin for ? weeks. Requirement of anticoagulant therapy with oral vitamin K antagonists; low-dose anticoagulants for maintenance of patency of central venous access devices or prevention of deep venous thrombosis is allowed; therapeutic use of low molecular weight heparin is allowed History of pulmonary embolus within months or deep venous thrombosis (DVT) within weeks of enrollment; patients on anticoagulation must be on a stable dose of warfarin with a therapeutic-range international normalized ratio (INR) or on a stable dose of low molecular weight heparin Patients must not have any evidence of bleeding diathesis or be on any therapeutic anticoagulation such as low molecular weight (LMW) heparin or warfarin for deep vein thrombosis (DVT) treatment History of pulmonary embolism or untreated deep venous thrombosis (DVT) within the past months; Note: Patients with recent DVT who have been treated with therapeutic anticoagulation including Coumadin or any low molecular weight heparin for at least weeks are eligible Patients receiving therapeutic anticoagulation; prophylactic anticoagulation of venous access devices is allowed; caution should be taken on treating patients with low dose heparin or low molecular weight heparin for deep vein thrombosis (DVT) prophylaxis during treatment with bevacizumab as there may be an increased risk of bleeding Concurrent or prior (within days of enrollment) anticoagulation therapy, except for the use of low dose coumarin-type anticoagulants or low molecular weight heparin for prophylaxis against central venous catheter thrombosis Pulmonary embolus or thrombosis of the deep venous system (deep vein thrombosis [DVT]) within weeks of starting study treatment; patients who had a history of thromboembolic disease should be stable on therapeutic anticoagulation using low molecular weight (LMW) heparin for at least weeks prior to the start of study treatment; use of warfarin (or derivatives) is not allowed at the start of study treatment Patient is in need of anticoagulation therapy except for low-dose heparin or low-dose coumadin for maintenance of patency of central venous access or prevention of deep vein thrombosis (DVT) History of therapeutic doses of anticoagulants including warfarin and low molecular weight heparin (e.g. for prior deep venous thrombosis and pulmonary embolisms) in the preceding year History of therapeutic doses of anticoagulants including warfarin and low molecular weight heparin (e.g. for prior deep venous thrombosis and pulmonary embolism) in the preceding year