Trial of Lapatinib and Weekly Paclitaxel for Advanced Urothelial Cancer

Inclusion Criteria: * Male and female patients must be at least 18 years of age. * Diagnosis of urothelial carcinoma that is locally advanced, recurrent or metastatic is required. * Patients must have progressed on prior regimens (1-2 allowed) of systemic chemotherapy for any stage of urothelial carcinoma (including peri-operative chemotherapy alone in which case they must have progressed within 12 months of peri-operative chemotherapy), with one of the regimens including a platinum agent. * Patients must have adequate tumor tissue (primary or metastatic tumor; fresh or archived) available for EGFR and HER2 expression analysis at baseline as determined by the study pathologist. * EGFR and HER2 status by Immunohistochemistry of a potential patient's urothelial tumor must be determined at baseline before registration or therapy. A potential patient's eligibility will depend on his/her tumor's EGFR and HER2 category AND the available open slots in that category at that time. * Patients must be able to care for themselves and must be up and about more than 50% of waking hours. * Patients must have measurable disease. * Prior chemotherapy or radiation therapy must have been completed prior to registration (at least 4 weeks prior for chemotherapy and at least 2 weeks prior for radiation). Patients must have recovered from any reversible side effects and must not have had more than 25% of the bone marrow irradiated. * Ability of the heart to pump blood must be adequate for this study. This will be determined by a screening test. * Patients must have adequate organ and marrow function as determined by screening tests. * All patients must be informed of the investigational nature of this study and must sign an informed consent document. * Both men and women and members of all races and ethnic groups are eligible for this trial. Exclusion Criteria: * No prior use of anti-HER2 (including trastuzumab) or anti-EGFR (including erlotinib, gefitinib, cetuximab) therapy, paclitaxel, nanoparticle bound paclitaxel or docetaxel for any reason. * Must not have history of or known spinal cord compression, or carcinomatous meningitis, or evidence of symptomatic brain or leptomeningeal disease. Patients with known brain metastases would be excluded from this clinical trial. * Known HIV positive patients may not participate. * No malignancy for which systemic therapy, surgery or radiation is ongoing or anticipated within the next 3 months as assessed by the investigator. * In situ carcinoma of any site including CIS of the urothelial tract \[or\] adequately treated basal cell or squamous cell skin cancer is allowed. * Patients with history of non-metastatic prostate cancer who have a PSA \<2 ng/mL with or without androgen deprivation therapy are eligible. * Patients with serious cardiac illness or medical conditions are excluded. * Patients must not receive treatment on another therapeutic clinical trial. Supportive care trials and non-interventional trials, e.g. quality of life (QOL) trials are allowed.. * Herbal medications or supplements are not allowed. * Female patients must be surgically sterile or be postmenopausal as per the investigator's discretion, or must agree to use effective contraception during the period of therapy. All female patients with reproductive potential must have a negative pregnancy test (serum or urine) prior to registration. Male patients must be surgically sterile or must agree to use effective contraception during the period of therapy. * Must not have malabsorption syndrome, any disease significantly affecting gastrointestinal function, or resection of the stomach or small bowel, or unable to swallow oral medication. * No history of allergic reactions to compounds of similar chemical or biologic composition to lapatinib. * Use of strong CYP3A4 inhibitors or inducers is prohibited on study.