DISEASE CHARACTERISTICS: - Histologically or cytologically confirmed HER2-positive (3+ by IHC or 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 - Must have estrogen-receptor (ER) and progesterone-receptor (PR)-negative metastatic breast cancer OR must have 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 MK2206/lapatinib combination must agree to undergo serial biopsies for research purposes - Tumor must be accessible for biopsy - 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 by conventional techniques or as ≥ 10 mm by spiral 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 with brain metastases are eligible if the brain metastases have been stable for at least one month and the patients are steroid-independent PATIENT CHARACTERISTICS: - Menopausal status not specified - ECOG performance status (PS) 0-2 (Karnofsky PS 60-100%) - Life expectancy > 12 weeks - WBC ≥ 3,000/mm³ - ANC ≥ 1,500/mm³ - Platelet count ≥ 100,000/mm³ - Total bilirubin normal - Magnesium normal - Potassium normal - AST/ALT ≤ 2.5 times upper limit of normal (ULN) - Creatinine ≤ 1.2 times ULN OR creatinine clearance ≥ 60 mL/min - Not pregnant or nursing - Negative pregnancy test - Women of child-bearing potential must agree to use two forms of contraception (hormonal, barrier method of birth control, or abstinence) prior to study entry, for the duration of study participation, and for 3 months after the last dose of study therapy - Able to swallow tablets - No preexisting cardiac conditions, including uncontrolled or symptomatic angina, arrhythmias, or congestive heart failure - Patients with residual drug-induced peripheral neuropathy ≤ grade 2 eligible provided that it has been stable and not worsening for at least 30 days - Patients who are HIV-positive are eligible if CD4 count ≥ 350 cells/mm³ and they are not undergoing HAART anti-retroviral therapy - No co-morbid condition(s) that, at the opinion of the investigator, prevent safe treatment - No history of hepatitis B or C positivity (active or previous therapy) - No requirement for chronic maintenance of white blood cell counts or granulocyte counts through the use of growth factor support (e.g., Neulasta®, Neupogen®) - No history of seizures - No history of allergic reactions attributed to compounds of similar chemical or biologic composition to MK2206, lapatinib, or other agents used in study - Diabetes or risk for hyperglycemia that has been well controlled on oral agents before entering the trial allowed - No baseline QTcF > 450 msec (male) or QTcF > 470 msec (female) - No 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 - No malabsorption syndrome or other condition that would interfere with intestinal absorption - No significant bundle branch block or bradycardia related to cardiac disease PRIOR CONCURRENT THERAPY: - See Disease Characteristics - More than 3 weeks since prior chemotherapy (6 weeks for nitrosoureas or mitomycin C) or radiotherapy and recovered to CTCAE ≤ grade 1 toxicities - No prior radiotherapy to ≥ 50% of total marrow volume - More than 30 days or five half lives (whichever is less) since prior experimental and immunotherapies and fully recovered from any acute effects of these therapies - No prior lapatinib ditosylate or an AKT inhibitor - Patients who have received an AKT inhibitor or lapatinib as part of a single or extremely limited dosing study, such as a phase 0 study, are allowed - Prior TDM-1 or anti-HER2 monoclonal antibody (i.e., trastuzumab, pertuzumab) allowed - No prior allogeneic stem cell transplantation - No concurrent HAART anti-retroviral therapy for HIV-positive patients - No concurrent medications that may cause QTc interval prolongation - No other concurrent anti-cancer therapy (cytotoxic, biologic, radiation, or hormonal other than for replacement) except for medications that are prescribed for supportive care but may potentially have an anti-cancer effect (i.e., megestrol acetate or bisphosphonates) that were started within a month prior to enrollment into study - Concurrent erythropoietin and darbepoetin allowed - No other concurrent investigational agents