Inclusion Criteria:  Phase I: histologically confirmed B-cell NHL, including marginal zone lymphoma, follicular lymphoma, mantle cell lymphoma, large B-cell lymphoma (including transformed marginal zone lymphoma [MZL], transformed follicular lymphoma [FL], Richter syndrome with absolute lymphocyte count [ALC] < 5,000 10^9/L, FL grade 3B, high grade B-cell lymphoma and primary mediastinal B-cell lymphoma), and composite lymphoma (concomitant indolent and aggressive B-NHL) Phase I: have failed at least one line of systemic therapy and not be eligible for known standard of care curative treatment option; patients with mantle cell lymphoma and aggressive B-cell lymphoma will need to have received 2 prior lines of systemic therapy Phase II: histologically confirmed follicular lymphoma, grade 1, 2, or 3a or marginal zone lymphoma Phase II: have had no prior systemic treatment for lymphoma  Phase II: high tumor burden disease, defined by meeting 1 or more of the following Groupe d'Etude des Lymphomes Folliculaires (GELF) criteria  Bulky disease defined as: a nodal or extranodal (except spleen) mass > 7 cm in its greater diameter or, involvement of at least 3 nodal or extranodal sites (each with a diameter greater than > 3 cm) Presence of at least one of the following B symptoms: fever (> 38 Celsius [C]) of unclear etiology, night sweats, weight loss greater than 10% within the prior 6 months Symptomatic splenomegaly Impending organ compression or involvement Any one of the following cytopenias due to lymphoma: hemoglobin < 10 g/dL (6.25 mmol/L), platelets < 100 x 10^9/L , or absolute neutrophil count (ANC) < 1.5 x 10^9 /L Pleural or peritoneal serous effusion (irrespective of cell content) Lactate dehydrogenase [LDH] > upper limit of normal (ULN) or beta 2 microglobulin > ULN Phase II: stage III or IV disease Bi-dimensionally measurable disease, with at least one nodal lesion >= 1.5 cm or one extra-nodal lesion >= 1 cm in longest diameter by computed tomography (CT), positron emission tomography (PET)/CT, and/or magnetic resonance imaging (MRI) Must be >= 18 years of age Eastern Cooperative Oncology Group (ECOG) performance status 0-1 Absolute neutrophil count (ANC) >= 1,000/mm^3, independent of growth factor support (within 28 days prior to signing informed consent) Platelet counts >= 75,000/mm^3 or >= 50,000/mm^3 if bone marrow involvement with lymphoma, independent of transfusion support for >= 14 days in either situation (within 28 days prior to signing informed consent) Hemoglobin > 8 g/dL, independent of transfusion support for >= 14 days (within 28 days prior to signing informed consent) Serum aspartate transaminase (AST) and alanine transaminase (ALT) < 2 x upper limit of normal (ULN) Creatinine clearance > 30 ml/min calculated by modified Cockcroft-Gault formula Total bilirubin < 1.5 x ULN unless bilirubin is due to Gilbert's syndrome, documented liver involvement with lymphoma, or of non-hepatic origin, in which case bilirubin should not exceed 3 g/dL Prothrombin time (PT)/international normalized ratio (INR) < 1.5 x ULN and partial thromboplastin time (PTT) < 1.5 x ULN Must be able to adhere to the study visit schedule and other protocol requirements Women of childbearing potential and men who are sexually active must be practicing a highly effective method of birth control during and after the study (females of childbearing potential: must either completely abstain from heterosexual sexual conduct or must use 2 methods of reliable contraception, 1 highly effective [intrauterine device, birth control pills, hormonal patches, injections, vaginal rings, or implants] and at least 1 additional method [condom, diaphragm, cervical cap] of birth control). Reliable contraceptive methods must be started at least 4 weeks before lenalidomide, and continued for at least 4 weeks after last dose of lenalidomide. Males who are sexually active must be practicing complete abstinence or agree to a condom during sexual contact with a pregnant female or female of child bearing potential. Men must agree to not donate sperm during the study and 28 days after the last dose of lenalidomide. For females, these restrictions apply at least 4 weeks before study treatment, during the period of therapy and for 120 days after the last dose of study drug. For males, these restrictions apply during the period of therapy and for 28 days after the last dose of study drug  Women of childbearing potential must have a negative serum (beta-human chorionic gonadotropin [beta-hCG]) pregnancy test at screening. Women who are pregnant or breastfeeding are ineligible for this study.  Females of reproductive potential must adhere to the scheduled pregnancy testing as required in the Revlimid Risk Evaluation and Mitigation Strategy (REMS) program Sign (or their legally-acceptable representatives must sign) an informed consent document indicating that they understand the purpose of and procedures required for the study, including biomarkers, and are willing to participate in the study All study participants must be registered into the mandatory Revlimid REMS program, and be willing and able to comply with the requirements of the REMS program  Exclusion Criteria:  Known active central nervous system lymphoma or leptomeningeal disease, except subjects with a history of central nervous system lymphoma treated and in remission > 6 months Burkitt lymphoma Chronic lymphocytic leukemia (CLL)/small lymphocytic lymphoma (SLL) or lymphoplasmacytic lymphoma (LPL)/Waldenstrom macroglobulinemia  Any prior history of other malignancy besides B-NHL, unless the patient has been free of disease for >= 3 years and felt to be at low risk for recurrence by the treating physician, except:  Adequately treated localized skin cancer without evidence of disease Adequately treated cervical carcinoma in situ without evidence of disease Any life-threatening illness, medical condition, or organ system dysfunction which, in the investigator's opinion, could compromise the subject's safety, interfere with the absorption or metabolism of lenalidomide capsules, or put the study outcomes at undue risk  Known history of human immunodeficiency virus (HIV), or active hepatitis C virus, or active hepatitis B virus infection, or any uncontrolled active significant infection, including suspected or confirmed JC virus infection and severe acute respiratory syndrome coronavirus 2 (SARS-CoV2)  Patients with inactive hepatitis B infection must adhere to hepatitis B reactivation prophylaxis unless contraindicated. Hepatitis B or C serologic status: subjects who are hepatitis B core antibody (anti-HBc) positive and who are surface antigen negative will need to have a negative polymerase chain reaction (PCR). Those who are hepatitis B surface antigen (HbsAg) positive or hepatitis B PCR positive will be excluded. Subjects who are hepatitis C antibody positive will need to have a negative PCR result. Those who are hepatitis C PCR positive will be excluded. Subjects with a history of hepatitis C who received antiviral treatment are eligible as long as PCR is negative History of immunodeficiency (with the exception of hypogammaglobulinemia) or concurrent systemic immunosuppressant therapy (e.g., cyclosporine, tacrolimus, etc., or chronic administration glucocorticoid equivalent of > 10 mg/day of prednisone) within 28 days of the first dose of study drug Known anaphylaxis or immunoglobulin (Ig)E-mediated hypersensitivity to murine proteins or to any component of ALX148, lenalidomide and/or rituximab Requires chronic treatment with strong CYP3A inhibitors, for a list of strong CYP3A inhibitors. If patients have been on a strong CYP3A inhibitor in the past, they will not be eligible if the CYP3A inhibitor was administered within 7 days of the first dose of study drug Clinically significant cardiovascular disease such as uncontrolled or symptomatic arrhythmias, congestive heart failure, or myocardial infarction within 6 months of screening, or any class 3 (moderate) or class 4 (severe) cardiac disease as defined by the New York Heart Association Functional Classification. Subjects with controlled, asymptomatic atrial fibrillation during screening can enroll on study Significant screening electrocardiogram (ECG) abnormalities including left bundle branch block, 2nd degree atrioventricular (AV) block, type II AV block, or 3rd degree block Active bleeding or known bleeding diathesis (e.g., von Willebrand's disease) or hemophilia History of stroke or intracranial hemorrhage within 6 months prior to study entry Vaccinated with live, attenuated vaccines within 4 weeks of study entry Lactating or pregnant subjects Administration of any investigational agent within 28 days of first dose of study drug Patients who have undergone major surgery within 28 days or minor surgery within 3 days of first dose of study drug Patients taking corticosteroids during the last 4 weeks, unless administered at a dose equivalent to < 10 mg/day prednisone (over these 4 weeks) Life expectancy < 6 months Neuropathy > grade 1 Prior exposure to lenalidomide or to a CD47/SIRP alpha antagonist/inhibitor, independently from indication Patient who received chimeric antigen receptor (CAR) T-cell therapy within 1 month, autologous stem cell transplant within 3 months, allogeneic stem cell transplant within 6 months Patients who have difficulty with or are unable to swallow oral medication, or have disease significantly affecting gastrointestinal function that would limit absorption of oral medication Uncontrolled autoimmune hemolytic anemia (AIHA) or idiopathic thrombocytopenic purpura (ITP) History of hemolytic transfusion reaction secondary to allo-antibodies Patients who have an active autoimmune disease that has required systemic treatment in past 2 years (i.e., with use of disease modifying agents, corticosteroids or immunosuppressive drugs). Replacement therapy (e.g., thyroxine, insulin, or physiologic corticosteroid replacement therapy for adrenal or pituitary insufficiency) is not considered a form of systemic treatment and is allowed Patients who have a history of (non-infectious) pneumonitis that required steroids or has current pneumonitis Known history of symptomatic deep vein thrombosis or pulmonary embolism Known history of Stevens-Johnson syndrome (SJS) or toxic epidermal necrolysis (TEN) or drug rash with eosinophilia and systemic symptoms (DRESS)