Radiation Therapy and Rituximab in Treating Patients With Stage I-II Grade 1 or Grade 2 Follicular Lymphoma

Inclusion Criteria: * Newly diagnosed patients with stage I and II follicular lymphoma, pathologically confirmed at MD Anderson Cancer Center (MDACC) to be grade 1 or 2 * Prophylactic use of lamivudine in patients that have antibody positive (+), but no active infection will be up to the treating physician * Absolute neutrophil count (ANC) \>= 1000/mm\^3; this value must be obtained within four weeks before protocol entry * Platelets \>= 80,000/mm\^3; this value must be obtained within four weeks before protocol entry * Hemoglobin \>= 8 g/dL; this value must be obtained within four weeks before protocol entry * Bilirubin =\< 1.5 times the upper limit of normal (ULN); this value must be obtained within four weeks before protocol entry * Alanine aminotransferase (ALT) =\< 2 times the ULN or aspartate aminotransferase (AST) =\< 2 times the ULN; these values must be obtained within four weeks before protocol entry * Performance status \>= 2 * Patients are required to have adequate renal function as indicated by a serum creatinine =\< 2.5 mg/dL; this value must be obtained within four weeks before protocol entry * No prior known allergic reaction to monoclonal antibodies * Male patients must agree to use a barrier method of contraception or agree to abstain from heterosexual activity for the duration of the study * Female patients must be willing to use two adequate barrier methods of contraception to prevent pregnancy or agree to abstain from heterosexual activity throughout the study or be post menopausal (free from menses \> two years or surgically sterilized) * Female patients of childbearing potential must have a negative serum pregnancy test (beta human chorionic gonadotropin \[B HCG\]) within 72 hours of receiving the first dose of rituximab * Patients must have the ability able to give informed consent Exclusion Criteria: * Patients with active hepatitis B and/or hepatitis C infection * Patients with known human immunodeficiency virus (HIV) infection * Patients with active infections requiring specific anti-infective therapy are not eligible until all signs of infections are resolved * Patients who had previous radiation dose to the site of the current primary disease, which would lead to violation of known radiation tolerance limit of that particular site if treated again * Patients with pre-existing cardiovascular disease requiring ongoing treatment; this includes: congestive heart failure III/IV as defined by New York Heart Association (NYHA); uncontrolled cardiac arrhythmia; unstable angina pectoris; and recent myocardial infarction (MI) (within 6 months) * Patients who are pregnant or breast-feeding * Patient with concurrent use of complementary or alternative medicines * Patients with psychiatric illness and/or social situations that would limit compliance with the study medication and requirements