Lapatinib With Trastuzumab in Treating Patients With HER2-Negative/HER2 Mutant Metastatic Breast Cancer

Inclusion Criteria: * Patient must have histologically or cytologically confirmed metastatic breast cancer * The breast cancer has been tested negative for HER2 (0 or 1+ by immunohistochemistry \[IHC\] or non-amplified by fluorescence in-situ hybridization \[FISH\]) * Patient may have measurable or evaluable disease * If given prior radiotherapy and/or prior chemotherapy, the patient must have completed radiation therapy and be at least 1 week from the last chemotherapy administration, with adequate recovery of bone marrow and organ functions, before starting lapatinib or trastuzumab \* Note that the HER2 sequencing analysis can be performed while patient is receiving other systemic therapies so the results could be used to determine whether the patient is eligible to receive lapatinib and trastuzumab when disease progresses from current therapy * Patient must have had at least one lines of systemic therapy for metastatic breast cancer * Patient must have disease that progressed on his/her most recent treatment regimen * Patient must be \> 18 years of age. * Patient must have an Eastern Cooperative Oncology Group (ECOG) performance status =\< 2 * Total bilirubin =\< 1.5 x institutional upper limit of normal (IULN) unless due to Gilbert's syndrome * Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase \[SGOT\])/alanine aminotransferase (ALT) (serum glutamic pyruvate transaminase \[SGPT\]) =\< 3.0 x IULN with/without liver metastases * Creatinine =\< 1.5 x IULN * Patient must have a left ventricular ejection fraction (LVEF) \>= institutional lower limit of normal (ILLN) to be eligible for study treatment; to avoid the cost of screening, patients with known recent LVEF \< LLN or symptoms of congestive heart failure are not eligible for registration * Women of childbearing potential (WOCBP) and men must agree to use adequate contraception (hormonal or barrier method of birth control, abstinence) prior to study entry and for the duration of study participation; should a woman become pregnant or suspect she is pregnant while participating in this study, she must inform her treating physician immediately * Patient (or legally authorized representative if applicable) must be able to understand and willing to sign an institutional review board (IRB) approved written informed consent document * Patients with known treated brain metastasis are eligible, but must have received radiation and be off steroids and stable for 3 months * Patients meeting all inclusion criteria listed above and exclusion criteria will be registered to undergo HER2 mutation analysis; only patients with mutations in HER2 either in the primary or metastatic tumor are eligible for study therapy with lapatinib and trastuzumab; those without mutations in HER2 are not eligible for study drug therapy; information and tissue collected from patients without HER2 mutations will be used for molecular epidemiology studies of HER2 negative breast cancer Exclusion Criteria: * Patient must not be receiving any other investigational agents * Patient must not have an uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements * Patient must not have acute or currently active/requiring antiviral therapy hepatic or biliary disease (with the exception of patients with Gilbert's syndrome, asymptomatic gallstones, liver metastases, or stable chronic liver disease per investigator assessment) * Patient must not be pregnant and/or breastfeeding * Patient must not have a history of significant cardiac disease, cardiac risk factors, or uncontrolled arrhythmias * Patient must not have symptomatic intrinsic lung disease or extensive tumor involvement of the lungs resulting in dyspnea at rest