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