Lapatinib Ditosylate and Akt Inhibitor MK2206 in Treating Women With Metastatic Breast Cancer

Inclusion Criteria: * Patients must be women with histologically or cytologically confirmed Her2 positive (3+ by immunohistochemistry \[IHC\] or fluorescence in situ hybridization \[FISH\] ratio \>= 2.0) advanced breast cancer that is metastatic or unresectable and for which standard curative or palliative measures do not exist or are no longer effective * Patients must have estrogen receptor (ER) and progesterone receptor (PR) negative metastatic breast cancer or have had progressive disease following at least 1 prior hormonal therapy for ER or PR positive metastatic breast cancer * Patients enrolled in the expansion cohort at the MTD dose of MK-2206/lapatinib combination must agree to undergo two biopsies for research purposes (Note: we will only biopsy the MTD cohort and their tumor must be accessible for biopsy) * Patients with brain metastases will be eligible if the brain mets have been stable for at least one month and the patients are steroid-independent * Patients must have measurable disease, defined as at least one lesion that can be accurately measured in at least one dimension (longest diameter to be recorded for non-nodal lesions and short axis for nodal lesions) as \>= 20 mm with conventional techniques or as \>= 10 mm with spiral computed tomography (CT) scan; patients with skin-only disease not measurable by RECIST are eligible but must have disease for which unilateral dimensions can be measured and must have monthly photographs with measurements available * Patients must have Eastern Cooperative Oncology Group (ECOG) performance status =\< 2 (Karnofsky \>= 60%; Merck \& Co. suggest ECOG performance status of 0-1 for trials with MK-2206, but inclusion of performance status 2 patients is at the discretion of investigators * Leukocytes \>= 3,000/mcL * Absolute neutrophil count \>= 1,500/mcL * Platelets \>= 100,000/mcL * Total bilirubin within normal institutional limits * Magnesium within normal institutional limits * Potassium within normal institutional limits * Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase \[SGOT\])/alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) =\< 2.5 x institutional upper limit of normal * Creatinine =\< 1.2 x institutional upper limit of normal OR creatinine clearance \>= 60 mL/min/1.73 m\^2 for patients with creatinine levels above institutional norm * Lapatinib has been reported to decrease left ventricle ejection fraction (LVEF); patients with preexisting cardiac conditions, including uncontrolled or symptomatic angina, arrhythmias, or congestive heart failure will not be eligible; normal LVEF will be confirmed before starting lapatinib, and evaluations (echocardiogram \[ECHO\]/multi gated acquisition scan \[MUGA\]) continued every 3 cycles during treatment; repeat LVEF determination will be performed for any signs or symptoms suggestive of congestive heart failure * Patients must have developed progressive disease following at least 1 prior systemic therapy for metastatic breast cancer * Prior chemotherapy is allowed; patients must not have received chemotherapy for 3 weeks prior to the initiation of study treatment and must have recovered to =\< Common Terminology Criteria for Adverse Events (CTCAE) grade 1 toxicities related to prior chemotherapy; patients must not have had nitrosoureas or mitomycin C for 6 weeks prior to the initiation of study treatment; patients who have alopecia (any grade) or residual drug-induced neuropathy of =\< grade 2 will be eligible if it has been stable, and not worsening, for at least 30 days; patients who have prior treatment with an AKT inhibitor will be excluded from participating in this study; patients are eligible if they had prior therapy with lapatinib UNLESS they are to be enrolled in the expansion cohort at the MTD dose of MK-2206/lapatinib; patients in the expansion cohort at the MTD dose of MK-2206/lapatinib who had prior treatment with lapatinib will be EXCLUDED * Prior radiation therapy is allowed; however, any radiation therapy must have occurred greater than 3 weeks from the planned initiation of study treatment and any radiation-induced toxicity must have recovered to =\< grade 1 at the time of initiation of study treatment; patients who have received prior radiation to 50% or more of their total marrow volume will be excluded * Prior experimental (non-Food and Drug Administration \[FDA\] approved) therapies and immunotherapies are allowed; patients must not have received these therapies for 30 days or five half-lives of the drug (whichever is less) prior to the initiation of study treatment and must have full recovery from any acute effects of these therapies; prior therapy with TDM-1 or anti-Her2 monoclonal antibodies (i.e. trastuzumab, pertuzumab) is allowed * Patients must not have received allogeneic stem cell transplant * Patients must not have co-morbid condition(s) that, at the opinion of the investigator, prevent safe treatment * Patients must not be pregnant or nursing * Patients who are human immunodeficiency virus positive (HIV+) are eligible if they have adequate CD4 counts (CD4 cell count of \>= 350 cells/mm\^3) and are not undergoing highly active antiretroviral therapy (HAART); patients must not have a history of hepatitis B+ or hepatitis C+ (active or previous treatment) * Life expectancy of greater than 12 weeks * Women of child-bearing potential must agree to use two forms of 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 she or her partner is participating in this study, the patient should inform the treating physician immediately * Ability to understand and the willingness to sign a written informed consent document Exclusion Criteria: * Patients who have had chemotherapy or radiotherapy within 3 weeks (4 weeks for those who received radiation therapy of \> 5% of their total marrow volume; 6 weeks for nitrosoureas or mitomycin C) prior to entering the study; or those who have not recovered to =\< CTCAE grade 1 toxicities related to prior therapy are not eligible to participate in this study with the exception of grade 2 peripheral neuropathy if it has been stable, and not worsening, for at least 30 days * Patients may not have received any other investigational agents or immunotherapies within the preceding 30 days or five half-lives of the drug (whichever is less) * Patients must not have received prior treatment with either an AKT inhibitor or lapatinib with the exception of patients who have been administered an AKT inhibitor or lapatinib as part of a single or extremely limited dosing study, such as a phase 0 study * Patients must not receive any other anti-cancer therapy (cytotoxic, biologic, radiation, or hormonal other than for replacement) while on this study except for medications that are prescribed for supportive care but may potentially have an anti-cancer effect (i.e. megestrol acetate, bisphosphonates); these medications must have been started 1 month prior to enrollment on this study; erythropoietin (Epo) and darbepoetin (Darbepo) are allowed * Patients may not be receiving any other investigational agents * Any patient requiring chronic maintenance of white blood cell counts or granulocyte counts through the use of growth factor support (e.g. Neulasta, Neupogen) * Patients with a prior history of seizures * Patients with known brain metastases are excluded from this clinical trial if the mets have been stable for less than one month and/or if they are on active steroid treatment * Patients with a history of allergic reactions attributed to compounds of similar chemical or biologic composition to MK-2206, lapatinib, or other agents used in study * Preclinical studies demonstrated the potential of MK-2206 for induction of hyperglycemia in all preclinical species tested; patients with diabetes or at risk for hyperglycemia are not to be excluded from trials with MK-2206, but the hyperglycemia should be well controlled on oral agents before the patient enters the trial * Preclinical studies indicated transient changes in corrected QT (QTc) interval during MK-2206 treatment; prolongation of QTc interval is potentially a safety concern while on MK-2206 therapy; patients with baseline QTcF \> 450 msec (male) or QTcF \>470 msec (female) will be excluded from entry on study; a list of medications that may cause QTc interval prolongation are listed, and should be avoided by patients entering on trial * 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 * Pregnant women are excluded from this study; breastfeeding should be discontinued if the mother is treated with MK-2206; these potential risks may also apply to other agents used in this study * HIV-positive patients on combination antiretroviral therapy are ineligible * Patients with malabsorption syndrome or other condition that would interfere with intestinal absorption; patients must be able to swallow tablets * Patients enrolled on the MTD cohort who do not have accessible tumor or who refuse serial biopsies * Due to a high incidence of bradycardia observed in early trials of MK-2206, patients with significant bundle branch block, or bradycardia related to cardiac disease, should be excluded from the trial