Osimertinib and Navitoclax in Treating Patients With EGFR-Positive Previously Treated Advanced or Metastatic Non-small Cell Lung Cancer

Inclusion Criteria: * Histologically confirmed non-squamous NSCLC, with incurable advanced or metastatic disease * Prior genotyping positive for an EGFR activating mutation (L858R, exon 19 deletion, G719X, L861Q) * Progression after prior treatment with an EGFR TKI; in addition to this one prior line of therapy, any additional prior lines of therapy are permitted; prior treatment with a third-generation EGFR TKI is allowed for the dose escalation phase, but is not permitted for the expansion cohort * Adequate archival tissue from a biopsy performed after progression of disease on previous EGFR TKI; or willing to undergo a new tumor biopsy prior to registration (for the dose escalation portion only this requirement can be waived if T790M status has already been determined using a local assay) * For the dose expansion portion only, patient must: 1) have a tumor which is EGFR-T790M positive and 2) be treatment naive to T790M-directed EGFR TKI (e.g. AZD9291, rociletinib, etc); T790M testing may be done locally or centrally on study, but if done locally, tissue must be available for central confirmation * Measurable disease per Response Evaluation Criteria in Solid Tumors (RECIST 1.1) * Any number of prior therapies are allowed * Age \>= 18 years. NSCLC is exceedingly rare in patients \< 18 years of age. Because no dosing or adverse event data are currently available on the use of AZD9291 in combination with navitoclax in patients \< 18 years of age, children are excluded from this study * Eastern Cooperative Oncology Group (ECOG) performance status =\< 1 (Karnofsky \>= 70%) * Patients must have the ability to swallow oral dosage forms * Life expectancy of greater than 3 months * Leukocytes \>= 3,000/mcL * Absolute neutrophil count \>= 1,500/mcL * Hemoglobin \>= 8.0 g/dL * Platelets \>= 100,000/mcL * Activated partial thromboplastin time (aPTT), prothrombin time (PT) =\< 1.2 x upper limit of normal (ULN) * Total bilirubin =\< 1.5 x ULN (patients with Gilbert's syndrome may have serum bilirubin \> 1.5 x ULN) * Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase \[SGOT\])/alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) =\< 3.0 x institutional ULN * Creatinine =\< 2.0 mg/dL OR * Creatinine clearance \>= 50 mL/min * The effects of AZD9291 and navitoclax on the developing human fetus are unknown; for this reason, women of child-bearing potential and men must agree to use adequate contraception using one of the methods listed below prior to study entry, for the duration of study participation, and for 3 months for women and 6 months for men following the date of the last dose of AZD9291 and/or navitoclax: * Total abstinence from sexual intercourse (minimum one complete menstrual cycle prior to study drug administration) * Vasectomized male subject or vasectomized partner of female subjects * Hormonal contraceptives (oral, parenteral, transdermal or vaginal ring) for at least 3 months prior to study drug administration; if the subject is currently using a hormonal contraceptive, she should also use a barrier method during this study and for 3 months after study completion * Intrauterine device (IUD) * Double-barrier method: male condom plus diaphragm or vaginal cap with spermicide (contraceptive sponge, jellies or creams) * Additionally, male subjects (including those who are vasectomized) whose partners are pregnant or might be pregnant must agree to use condoms for the duration of the study and 6 months following completion of therapy * Women of childbearing potential must have a negative urine pregnancy test within 7 days prior to initiation of treatment; women will be considered not of childbearing potential if they are surgically sterile (bilateral oophorectomy or hysterectomy) and/or post-menopausal (amenorrheic for at least 12 months) * Should a woman become pregnant or suspect she is pregnant while she or her partner is participating in this study, she should inform her treating physician immediately * Patients with a prior history of brain metastases are eligible provided: * The brain metastases have been treated * The patient is asymptomatic from the brain metastases * Corticosteroids prescribed for the management of brain metastases have been discontinued at least 7 days prior to registration * The brain metastases are stable on pre-registration imaging * Patients must have completed last chemotherapy \>= 3 weeks or radiotherapy \>= 2 weeks prior to receiving study drugs * Patients must have recovered from adverse events attributable to previous treatment to =\< grade 1, except for alopecia and sensory neuropathy =\< grade 2 * Ability to understand and the willingness to sign a written informed consent document Exclusion Criteria: * Major surgery within 21 days of starting protocol treatment * Patients must discontinue previous EGFR-TKI at least 7 days prior to study enrollment * Patients who are receiving any other investigational agents * Past medical history of interstitial lung disease, drug-induced interstitial lung disease, radiation pneumonitis requiring steroid treatment, or any evidence of clinically active interstitial lung disease * Patients currently receiving (or unable to stop use at least 1 week prior to receiving the 1st dose of AZD9291) medications or herbal supplements known to be potent inhibitors of cytochrome P450, family 2, subfamily C, polypeptide 8 (CYP2C8) and potent inhibitors or inducers of cytochrome P450, family 3, subfamily A, polypeptide 4 (CYP3A4) are ineligible; patients are eligible if they stop use of these compounds at least 1 week prior to receiving any treatment on this protocol * Patients receiving anticoagulation or anti-platelet therapy are excluded due to the risk of thrombocytopenia with navitoclax; excluded agents include heparin or low molecular weight heparin, warfarin, clopidogrel, ibuprofen and other nonsteroidal anti-inflammatory drug (NSAIDS), tirofiban, and other anticoagulants, drugs, or herbal supplements that affect platelet function; administration of heparin to keep subject's infusion lines patent is allowed; low-dose anticoagulation medications that are used to maintain the patency of a central intravenous catheter are allowed; aspirin will not be allowed within 7 days prior to the first dose of navitoclax or during navitoclax administration; however, subjects who have previously received aspirin therapy for thrombosis prevention, may resume a low dose (i.e., maximum 100 mg QD) of aspirin if platelet counts are stable (\>= 50,000/mm\^3) through 6 weeks of navitoclax administration; all decisions regarding treatment with aspirin therapy will be determined by the investigator in conjunction with the medical monitor * Patients with an underlying condition predisposing them to bleeding or currently exhibiting signs of clinically significant bleeding * Patients with a recent history of non-chemotherapy-induced thrombocytopenic-associated bleeding within 1 year prior to the first dose of study drug * Patients with a significant history of cardiovascular disease (e.g., myocardial infarction \[MI\], thrombotic or thromboembolic event in the last 6 months) * Any of the following cardiac criteria: * Mean resting corrected QT interval (QTc using Frederica's formula \[QTcF\]) \> 470 msec * Any clinically important abnormalities in rhythm, conduction or morphology of resting electrocardiogram (ECG) (e.g., complete left bundle branch block, third degree heart block, second degree heart block) * Congenital long QT syndrome or family history of long QT syndrome * Patients with active malignancies other than NSCLC or patients with prior curatively treated malignancy at high risk of relapse during the study period with the exception of localized squamous or basal cell skin cancers * Patients with uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, gastrointestinal disease limiting absorption of AZD9291 such as a malabsorption syndrome or inflammatory bowel disease or psychiatric illness/social situations that would limit compliance with study requirements * Pregnant women are excluded from this study because AZD9291 and navitoclax have the potential for teratogenic or abortifacient effects; because there is an unknown but potential risk for adverse events in nursing infants secondary to treatment of the mother with AZD9291 and navitoclax, breastfeeding should be discontinued if the mother is treated with AZD9291 and navitoclax * History of hypersensitivity to AZD9291 (or drugs with a similar chemical structure or class to AZD9291) or any excipients of these agents * Patients with human immunodeficiency virus (HIV) on antiretroviral therapy are ineligible because of the potential for pharmacokinetic interactions with AZD9291