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. Patients with
             EGFR/ALK/ROS1 rearrangements should have received an FDA-approved TKI prior to
             enrollment on this trial.

          -  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 (eg, 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