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