Dasatinib and Lapatinib Ditolsylate in Treating Patients With Advanced Solid Tumors That Cannot Be Removed By Surgery

Inclusion Criteria: * Histologic proof of cancer that is now unresectable and refractory to or refused all standard treatment for the disease * Please contact study investigator and/or consult protocol document for specific details on laboratory criteria * Ability to provide informed consent * Willingness to return to Mayo Clinic for follow up * Life expectancy \>= 12 weeks * Negative serum pregnancy test done =\< 7 days prior to registration for women of childbearing potential only * Echocardiogram with ejection fraction \> 50% * ECOG performance status (PS) 0-2 * Able to swallow pills whole (patients with feeding tubes may be eligible if whole pills can be taken and tolerated through the feeding tube) * Willingness to provide the biologic specimens as required by the protocol for Cohort II, (MTD) patients only Exclusion Criteria: * Failure to fully recover from acute, reversible effects of prior chemotherapy regardless of interval since last treatment * Pregnant women * Any of the following prior therapies: chemotherapy =\< 4 weeks prior to registration; mitomycin C/nitrosoureas =\< 6 weeks prior to registration; immunotherapy =\< 4 weeks prior to registration; biologic therapy =\< 4 weeks prior to registration * Patients who have been treated with Avastin, Herceptin, or Erbitux are eligible if last treatment is \>= 4 weeks; molecularly targeted agents (erlotinib, sunitinib, sorafenib, gefitinib, imatinib) =\< 4 weeks prior to registration; radiation therapy =\< 4 weeks prior to registration; radiation to \> 25% of bone marrow * CNS metastases that are not stable for at least 4 weeks prior to registration based on imaging, clinical assessment, and use of steroids * Men or women of childbearing potential who are unwilling to employ adequate contraception throughout the study and until 4 weeks following study * Other concurrent chemotherapy, immunotherapy, radiotherapy, or any ancillary therapy considered investigational (utilized for a non-FDA-approved indication and in the context of a research investigation) * Current therapy with a CYP3A4 inhibitor or inducer * Known standard therapy for the patient's disease that is not refractory to treatment that is potentially curative or definitely capable of extending life expectancy * Uncontrolled pleural or pericardial effusion of any grade * Uncontrolled angina, congestive heart failure or MI within 6 months prior to registration * Diagnosed congenital long QT syndrome * Any history of clinically significant ventricular arrhythmias (such as ventricular tachycardia, ventricular fibrillation, or Torsades de pointes) * Prolonged QTc interval on pre-entry electrocardiogram (\> 450 msec) * Subjects with potassium or magnesium that are not within normal limits and cannot be corrected prior to registration * New York Heart Association classification III or IV * Diagnosed acquired bleeding disorder within one year (e.g., acquired anti-factor VIII antibodies) * Ongoing or recent (=\< 3 months prior to registration) significant gastrointestinal bleeding * Prophylactic use of colony-stimulating factors during the study is not allowed * Diagnosed congenital bleeding disorders (e.g., von Willebrand's disease) * G.I conditions that may interfere with drug absorption such as Ulcerative Colitis, Crohn's Disease, and Short Bowel Syndrome * Active hepatic or biliary disease (with the exception of patients with Gilbert's syndrome, asymptomatic gallstones, liver metastases or stable chronic liver disease per investigator's assessment) * Nursing women * Uncontrolled infection * Seizure disorder