Inclusion Criteria:

• Recurrent or progressive advanced stage non-small cell lung cancer (no small cell component) with most recent treatment being an FDA approved immune checkpoint inhibitor (pembrolizumab, atezolizumab, or nivolumab).
  • NOTE: Pathology reports documenting the diagnosis of NSCLC are required to be reviewed to confirm outside diagnosis.
• Sufficient tumor tissue available from original diagnosis or subsequent biopsy for analysis of estrogen receptor and aromatase.
• Tumor block or a minimum of 5 unstained slides.
• Failed at least 1 prior FDA approved treatment for advanced NSCLC. 
• Measureable disease by RECIST version 1.1.
• Post-menopausal defined as:
  • Age ≥ 55 years and 1 year or more of amenorrhea;
  •  Age < 55 years and 1 year or more of amenorrhea with an estradiol assay < 20 pg/mL;
  • Surgical menopause with bilateral oophorectomy.
• ECOG performance status 0, 1 or 2.
• Life expectancy of 3 months or more in the opinion of the enrolling investigator and documented in the medical record. 
• Adequate organ function within 14 days of study enrollment defined as: 
• Hematology:
  • Absolute neutrophil count (ANC) ≥ 1500/mm³;
  • Platelets ≥ 100,000/mm³;
  • Hemoglobin ≥ 8 g/dL.
• Biochemistry: 
  • Total Bilirubin within normal institutional limits.
  • AST/SGOT and ALT/SGPT ≤ 2.5 x upper limit of normal (ULN), except if there is known hepatic metastasis, wherein transaminases may be ≤ 5 x institutional ULN.
  • Serum creatinine ≤ 1.5 mg/dl or glomerular filtration rate > 50 ml/min.
• Must have recovered to CTCAE v 4 Grade 1 or better from the acute effects of any prior surgery, chemotherapy or radiation therapy. Chronic residual toxicity (i.e., peripheral neuropathy) is permitted. 
• A minimum time period must elapse between the end of a previous treatment and start of study therapy: 
  • 1 week from the completion of radiation therapy for brain metastases;
  • 4 weeks from the completion of chemotherapy or any experimental therapy;
  • 4 weeks from prior major surgery (such as open biopsy or significant traumatic injury).
• Voluntary written consent before any research related procedures or therapy.

Exclusion Criteria:

• Known active CNS disease.
• If patient has history of brain metastases, the brain lesions must have been treated with radiation and/or surgery.
• Patients should be neurologically stable and requiring ≤ 10mg oral prednisone equivalence of steroids per day.
• Any toxicity from immune-related toxicity from prior immune therapy that would preclude further treatment with anti-PD-1/PDL-1 inhibitor or ongoing IR toxicity ≥ Grade 2.
• Requiring > 10 mg prednisone equivalence of steroids per day for immune-related toxicity.
• Inability or unwilling to swallow study drug.
• Any gastrointestinal condition causing malabsorption or obstruction (e.g., celiac sprue, gastric bypass surgery, strictures, adhesions, history of small bowel resection, blind loop syndrome).
• Currently using hormone replacement therapy (oral or patch) or/and phytoestrogen supplements (i.e., black cohosh).
• Known hypersensitivity to exemestane or its excipients.
• Any serious underlying medical condition that, in the opinion of the enrolling physician, would impair the ability of the patient to receive protocol treatment.
• Prior malignancy, with the exception of curatively treated squamous cell or basal carcinoma of the skin or in situ cervical cancer, unless there is a 3-year disease-free interval.
• Concomitant use of strong CYP3A4 inducers such as rifampicin, phenytoin, carbamazepine, phenobarbital, or St. John's wort as these may significantly reduce the availability of exemestane.