Selumetinib in Treating Patients With Relapsed or Refractory Diffuse Large B-cell Lymphoma

Inclusion Criteria: * Voluntary written informed consent before performance of any study-related procedure not part of normal medical care, with the understanding that consent may be withdrawn by the subject at any time without prejudice to future medical care * Relapsed or refractory diffuse large B-cell lymphoma (transformed large cell lymphomas are allowed to enroll) * Patients must have received at least one previous therapeutic regimen, and no more than 6 previous therapeutic regimens * Eastern Cooperative Oncology Group (ECOG) performance status of 0, 1, or 2 * Life expectancy \> 3 months * No chemotherapy, radiation therapy, immunotherapy, or experimental anticancer therapy within 28 days before beginning study treatment * Human immunodeficiency virus (HIV)-positive patients are eligible if: the cluster of differentiation (CD)4 count is \> 400, have no acquired immune deficiency syndrome (AIDS)-defining illnesses (other than non-Hodgkin lymphoma \[NHL\]), and they are not taking combination antiretroviral therapy (cART) at the time of study entry that would interfere with cytochrome P450, family 3, subfamily A, polypeptide 4 (CYP4503A4) * No other active infection * Women of child-bearing potential and men must agree to use adequate contraception (hormonal or barrier method of birth control, or abstinence) prior to study entry, for the duration of study participation, and for 4 weeks after dosing with AZD6244 hyd-sulfate ceases; women of child-bearing potential must have a negative pregnancy test prior to entry; should a woman become pregnant or suspect she is pregnant while she or her partner participating in this study, the patient should inform her treating physician immediately; please note that the AZD6244 hyd-sulfate manufacturer recommends that adequate contraception for male patients should be used for 16 weeks post-last dose due to sperm life cycle * Pregnant women are excluded from this study; breastfeeding should be discontinued if the mother is treated with AZD6244 hyd-sulfate * Patients may have received prior autologous, but not prior allogeneic stem cell transplant; however, patients who are eligible for potentially curative treatment with bone marrow transplant should not be entered on this investigational trial, unless they refuse the transplant option (or are not eligible for transplantation) Exclusion Criteria: * Any prior exposure to mitogen-activated protein kinase kinase (MEK), Ras, or v-raf murine sarcoma 3611 viral oncogene homolog (Raf) inhibitors * Patients with any active central nervous system (CNS) involvement by lymphoma are excluded * Patients that are taking drugs that alter CYP450 3A4 (or cannot be changed to drugs that do not alter CYP450 3A4) are excluded * Cardiac conditions as follows: * Uncontrolled hypertension (blood pressure \[BP\] \>= 150/95 despite optimal therapy) * Heart failure New York Heart Association (NYHA) class II or above * Prior or current cardiomyopathy * Baseline left ventricular ejection fraction (LVEF) =\< 50% * Atrial fibrillation with heart rate \> 100 beats per minute (bpm) * Unstable ischemic heart disease (myocardial infarction \[MI\] within 6 months prior to starting treatment, or angina requiring use of nitrates more than once weekly) * Patients are excluded if there is corrected QT (QTc) interval \> 450 msecs or other factors that increase the risk of QT prolongation or arrhythmic events (e.g., heart failure, hypokalemia, family history of long QT interval syndrome) * Patients are excluded if they are taking any drugs that may significantly prolong the QTc; these drugs are prohibited during the study; if the patient is taking one or more of these medications, they may enroll if all pertinent medications are stopped with the associated "wash out" periods * Absolute neutrophil count (ANC) \< 1.5 x 10\^9/L (1500 per mm\^3) * Platelets \< 100 x 10\^9/L * Hemoglobin (Hgb) \< 8.0 g/dL * Serum bilirubin \>= 1.5 x upper limit of normal (ULN) * Aspartate aminotransferase (AST/serum glutamic oxaloacetic transaminase \[SGOT\]) or alanine aminotransferase (ALT/serum glutamate pyruvate transaminase \[SGPT\]) \>= 2.5 x ULN (\>= 5 ULN in presence of liver metastases) * There should be a minimum of a 1 month wash-out interval from another investigational product to AZD6244 hyd-sulfate dosing start plus recovery from side effects of investigational product * There should be a minimum of a 1 month wash-out interval from the end of previous systemic treatment and radiotherapy * Patients are excluded if there is a history of a serious medical or psychiatric illness likely to interfere with participation in this clinical study * Patients may not have recent history of refractory nausea and vomiting, chronic gastrointestinal diseases (e.g., inflammatory bowel disease), or significant bowel resection that would preclude adequate absorption