Lapatinib Ditosylate in Treating Patients With Unresectable Liver or Biliary Tract Cancer

Inclusion Criteria: * Histologically confirmed diagnosis of 1 of the following: * Hepatocellular carcinoma (hepatoma) * Child-Pugh classification score ≤ 7 * Biliary tract carcinoma * Surgically unresectable disease * Measurable disease * At least 1 unidimensionally measurable lesion ≥ 20 mm by conventional techniques OR ≥ 10 mm by spiral CT scan * Fresh tissue or paraffin embedded tissue from tumor blocks available * No ampulla of Vater tumors * No known brain metastases * Performance status - ECOG 0-1 * Performance status - Karnofsky 60-100% * More than 12 weeks * Absolute neutrophil count ≥ 1,500/mm\^3 * Platelet count ≥ 75,000/mm\^3 * Bilirubin ≤ 2 times upper limit of normal (ULN) * AST and ALT ≤ 3 times ULN * Albumin ≥ 2.5 mg/dL * INR ≤ 1.5 (for patients not receiving an anticoagulant) * Live metastases or stable chronic liver disease allowed * No current active hepatic or biliary disease except for Gilbert's syndrome or asymptomatic gallstone * Creatinine ≤ 2 mg/dL * Ejection fraction normal by echocardiogram or MUGA * No unstable angina pectoris * No cardiac arrhythmia * Able to swallow and retain oral medication * No gastrointestinal (GI) tract disease resulting in an inability to take oral medication * No malabsorption syndrome * No requirement for IV alimentation * No uncontrolled inflammatory GI disease (e.g., Crohn's disease or ulcerative colitis) * Not pregnant or nursing * Negative pregnancy test * Fertile patients must use effective contraception * No significant traumatic injury within the past 3 weeks * No active or ongoing infection * No history of allergic reaction attributed to compounds of similar chemical or biological composition to lapatinib * No psychiatric illness or social situation that would preclude study compliance * No other uncontrolled illness * No other malignancy within the past 3 years except adequately treated basal cell or squamous cell skin cancer or carcinoma in situ of the cervix * More than 4 weeks since prior biologic therapy * More than 4 weeks since prior immunotherapy * See Radiotherapy * More than 4 weeks since prior chemotherapy (6 weeks for nitrosoureas or mitomycin) * No prior cumulative doxorubicin dose \> 450 mg/m\^2 * At least 14 days since prior and no concurrent glucocorticoids (e.g., dexamethasone or equivalent \[dose \> 1.5 mg/day\]) * More than 4 weeks since prior radiotherapy * More than 12 weeks since prior radiotherapy with or without a fluoropyrimidine as a radiosensitizer (for patients with biliary carcinoma only) * No prior surgical procedure affecting absorption * More than 3 weeks since prior major surgery * Recovered from all prior therapy * No more than 1 prior systemic anticancer therapy, including chemoembolization * No prior epidermal growth factor receptor-targeting therapy * More than 6 weeks since prior cryotherapy, radiofrequency ablation, ethanol injection, transarterial chemoembolization, or photodynamic therapy AND meets both of the following criteria: * Indicator lesion is outside the area of prior treatment OR there is clear evidence of disease progression associated with the sole indicator lesion * Edges of indicator lesion are clearly distinct by CT scan * At least 7 days since prior and no concurrent H2 inhibitors or proton pump inhibitors * Concurrent antacids allowed provided they are administered \> 1 hour before and \> 1 hour after study drug administration * At least 7 days since prior and no concurrent CYP3A4 inhibitors, including any of the following: * Clarithromycin * Erythromycin * Troleandomycin * Delaviridine * Ritonavir * Indinavir * Saquinavir * Nelfinavir * Amprenavir * Lopinavir * Itraconazole * Ketoconazole * Voriconazole * Fluconazole (doses ≤ 150 mg/day are allowed) * Nefazodone * Fluvoxamine * Verapamil * Diltiazem * Cimetidine * Aprepitant * Grapefruit and grapefruit juice * Bitter orange * At least 6 months since prior and no concurrent amiodarone * At least 14 days since prior and no concurrent CYP3A4 inducers, including any of the following: * Phenytoin * Carbamazepine * Phenobarbital * Oxcarbazepine * Efavirenz * Nevirapine * Rifampin * Rifabutin * Rifapentine * Roxithromycin * Telithromycin * Hypericum perforatum (St. John's wort) * Modafinil * No concurrent combination antiretroviral therapy for HIV-positive patients * No other concurrent investigational agents * No other concurrent anticancer therapy * Concurrent oral anticoagulants (e.g., coumadin or warfarin) allowed provided there is increased vigilance in monitoring INR