Dasatinib in Treating Patients With Solid Tumors or Lymphomas That Are Metastatic or Cannot Be Removed By Surgery

Inclusion Criteria: * Patients must have histologically or cytologically confirmed solid tumor or lymphoma that is metastatic or unresectable and for which standard curative or palliative measures do not exist or are no longer effective; patients with a liver mass, elevated alpha-fetoprotein level (\>= 500 ng/mL) and positive serology for viral hepatitis, consistent with a diagnosis of hepatocellular carcinoma will be eligible without the need for pathologic confirmation of the diagnosis; all solid and lymphoma tumor types are eligible * Patients must have measurable or non-measurable disease; x-rays and/or scans for disease assessment must have been completed within 28 days (for measurable disease) or 42 days (for non-measurable disease) prior to registration; all disease must be assessed and documented on the web-based Baseline Tumor Assessment Form * Patients with brain metastases who require corticosteroids must be on stable or decreasing dose of corticosteroids; patients with known brain metastases must have had brain irradiation (whole brain or gamma knife); patients with untreated (non-irradiated) brain metastases are not eligible; patients on enzyme-inducing anticonvulsant medications (e.g. phenobarbital, phenytoin or carbamazepine) are not eligible * Patients must not be taking H2-receptor antagonists such as cimetidine, ranitidine, and famotidine, or any proton pump inhibitors, such as omeprazole, lansoprazole, esomeprazole, and pantoprazole; patients must stop these medications within 7 days prior to starting treatment * Patients must not have had anticancer therapy including chemotherapy, radiotherapy, immunotherapy, or investigational agent within 4 weeks prior to registration, except for targeted agents with half-life known to be \< 24 hours; patients must not have had targeted agents with half-life \< 24 hours within 2 weeks prior to registration; patients also must have recovered from serious adverse events due to agents administered within these acceptable time frames * Patients must not be planning to receive concurrent radiation, other chemotherapy, immune therapy or any other investigational agents for malignancy while receiving protocol treatment; hormonal treatment for prostate carcinoma may be continued and bisphosphonate treatment for bone disease is permitted * Patient must not have received prior therapy with dasatinib (BMS-354825) * Patients for whom there is a strong suspicion of being allergic to dasatinib because of a history of allergic reactions to similar compounds are not eligible * Patients must not have had major surgical procedures within the last 4 weeks prior to the first planned dose of study drug * Patients must not be taking therapeutic doses of anticoagulants; low dose warfarin for port prophylaxis is permitted * Zubrod performance status of 0-2 * Patients may not have any clinically significant cardiovascular disease including the following: * Myocardial infarction or ventricular tachyarrhythmia within 6 months * Prolonged corrected QT interval (QTc) \>= 480 msec (Fridericia correction) * Ejection fraction less than institutional normal * Major conduction abnormality (unless a cardiac pacemaker is present) * Patients with any cardiopulmonary symptoms of unknown cause (e.g. shortness of breath, chest pain, etc.) should be evaluated by a baseline echocardiogram with or without stress test as needed in addition to electrocardiogram (EKG) to rule out QTc prolongation; the patient may be referred to a cardiologist at the discretion of the principal investigator; patients with underlying cardiopulmonary dysfunction should be excluded from the study * Absolute neutrophil count \>= 1.5 x 10\^9/L * Platelets \>= 100 x 10\^9/L * Magnesium \>= lower limit of normal (LLN) * Potassium \>= LLN * Creatinine =\< 1.5 x upper limit of normal (ULN) OR calculated creatinine clearance \>= 60 mL/min/1.73 m\^2; if less than the normal range, supplementation should be initiated in the manner deemed appropriate by the treating physician * Patients with abnormal liver function are eligible and will be grouped according to the criteria; no distinction will be made between liver dysfunction due to metastases and liver dysfunction due to other causes; for patient registration, liver function tests (total bilirubin, aspartate aminotransferase \[AST\]/alanine aminotransferase \[ALT\], prothrombin time \[PT\]/international normalized ratio \[INR\] and partial thromboplastin time \[PTT\], and alkaline phosphatase) must be performed within 14 days prior to registration; for patient stratification, liver function tests must be performed within 72 hours of anticipated starting time of protocol treatment; patients must be stratified and treated based on the liver function tests performed within 72 hours prior to treatment; the South West Oncology Group (SWOG) Data Operations Center must be notified in writing in cases where the patient's cycle 1 pre-treatment liver function tests result in stratification to a dysfunction group different from how the patient was classified at registration * Patients with biliary obstruction for which a shunt has been placed are eligible, provided the liver function tests have stabilized (two measurements at least two days apart that put the patient in the same hepatic dysfunction stratum will be accepted as evidence of stable hepatic function); there must be no evidence of biliary sepsis and at least 2 weeks must have elapsed after the placement of a biliary shunt * Patients must not be pregnant or nursing; women/men of reproductive potential must have agreed to use an effective contraceptive method; since interaction with dasatinib and oral contraceptives is possible, a barrier method should be used and oral contraceptives are not permitted; a negative pregnancy test is required within 72 hours prior to starting therapy for women of reproductive potential; a woman is considered to be of "reproductive potential" if she has had menses at any time in the preceding 12 consecutive months; in addition to routine contraceptive methods, "effective contraception" also includes heterosexual celibacy and surgery intended to prevent pregnancy (or with a side-effect of pregnancy prevention) defined as a hysterectomy, bilateral oophorectomy or bilateral tubal ligation; however, if at any point a previously celibate patient chooses to become heterosexually active during the time period for use of contraceptive measures outlined in the protocol, he/she is responsible for beginning contraceptive measures * Patients who have experienced any of the following within the 12 months prior to starting protocol treatment are not eligible: myocardial infarction, severe/unstable angina, coronary/peripheral artery bypass graft, congestive heart failure, cerebrovascular accident including transient ischemic attack, or significant pulmonary embolus * Patients with ongoing cardiac dysrhythmias of NCI Common Terminology Criteria for Adverse Events (CTCAE) grade \>= 2, atrial fibrillation of any grade, or QTc interval \> 470 msec for females or \> 450 msec for males are not eligible * Patients with baseline pleural effusion are not eligible * Patients must not have active gastrointestinal bleeding * Patients with the inability to take oral medications, with a diagnosis of malabsorption syndromes or with significant bowel resection affecting absorption are not eligible * Patients with a clinically significant pleural effusion/ fluid retention/pericardial effusion are not eligible; patients with a history of pleurodesis and previous pleural effusion (malignant or non-malignant) may be eligible but treated with caution; patients with previous history of ascites may be treated * Patients with uncontrolled serious intercurrent medical illness including, but not limited to ongoing or serious active infection, symptomatic congestive heart failure, unstable angina pectoris, serious cardiac arrhythmia, uncontrolled diarrhea or psychiatric illness/social situations that would limit compliance with study requirements are not eligible * Patients known to be human immunodeficiency virus (HIV)-positive are not eligible; however, patients will not routinely be screened for HIV * Patients must be willing to undergo pharmacokinetic sampling * Patients or their legally authorized representative must be informed of the investigational nature of this study and must sign and give written informed consent in accordance with institutional and federal guidelines * At the time of patient registration, the treating institution's name and identification (ID) number must be provided to the Statistical Center in order to ensure that the current (within 365 days) date of institutional review board approval for this study has been entered into the data base