Combination of Osimertinib and Aspirin to Treat 1st Generation EGFR-TKI Resistance in NSCLC

Inclusion Criteria: * Patients must have Histologically or cytologically confirmed non small cell carcinoma of the lung who harbors EGFR-mutation and are previously disease progression to 1st generation EGFR-TKI. * Patient must have measurable stage IV disease (includes M1a, M1b stages or recurrent disease) (according to the 7th edition of the tumor node metastasis (TNM) classification system). However, patients with T4NX disease (stage III B) with nodule(s) in ipsilateral lung lobe are not eligible, because such patients were not included in historical controls. * Patients be age \>18 years and \< 75 years. * Patients must have a Life Expectancy of greater than 12 weeks. * Patients must have an electrocorticography (ECOG) performance status 0 or 1 (Karnofsky \> 70). * Patients must have normal organ and marrow function as defined below, within one week prior to randomization: absolute neutrophil count \>1,500/mL platelets \> 100,000/mL total bilirubin: within normal institutional limits AST(SGOT)/ALT(SGPT) \< 2.5 X institutional upper limit of normal creatinine \< 1.5 X institutional upper limit of normal urine dipstick for proteinuria of \< less than 1+. If urine dipstick is \> 1+ then a 24 hour urine for protein must demonstrate \< 500 mg of protein in 24 hours to allow participation in the study. * Women of child-bearing potential 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 should inform her treating physician immediately. * Patients must have an international normalized ratio (INR) \< 1.5 and a partial thromboplastin time (PTT) no greater than upper limits of normal within 1 week prior to randomization. * Patients with a history of hypertension must be well-controlled (\<150 systolic/\<100 diastolic) on a stable regimen of anti-hypertensive therapy. * Patients must have the ability to understand and the willingness to sign a written informed consent document. Exclusion Criteria: * Patients with uncontrolled intercurrent illness including, but not limited to, ongoing or active infection,symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia,gastric ulcer,hemophilia,thrombopenia,active hemorrhage,podagra,kidney failure or psychiatric illness/social situation that would limit compliance with study requirements. * Patients receiving chronic daily treatment with aspirin (\> 325 mg/day) or nonsteroidal anti-inflammatory agents known to inhibit platelet function. Treatment with dipyridamole (Persantine), ticlopidine (Ticlid),clopidogrel (Plavix) and/or cilostazol (Pletal)is also not allowed. * Patients receiving therapeutic anticoagulation. Prophylactic anticoagulation of venous access devices is allowed provided Section 3.10 is met. Caution should be taken on treating patients with low dose heparin or low molecular weight heparin for DVT prophylaxis during treatment with bevacizumab as there may be an increased risk of bleeding. * Prior use of chemotherapy. * Patients receiving immunotherapy, hormonal-therapy and or radiotherapy within 2 weeks prior to entering the study. Note: Those who have not recovered from adverse events due to these agents administered will be considered ineligible. * Patients receiving any other investigational agents. * Patients with uncontrolled brain metastasis. Note: Patients with brain metastases must have stable neurologic status following local therapy (surgery or radiation) for at least 2 weeks, and must be without neurologic dysfunction that would confound the evaluation of neurologic and other adverse events. * Patients with a history of allergic reactions attributed to compounds of similar chemical or biologic composition to Osimertinib and Aspirin or other agents used in the study are excluded. * Women that are pregnant or breastfeeding Note: Pregnant women are excluded from this study because the agents used in this study may be teratogenic to a fetus. Because there is an unknown but potential risk for adverse events in nursing infants secondary to treatment of the mother with paclitaxel, breastfeeding women are also excluded from this study. * Patients that are HIV-positive on combination antiretroviral therapy due to the potential for lethal infections when treated with marrow-suppressive therapy.