An Open Label, Randomized, Multicenter Study Comparing the Efficacy and Safety of the Combination of Lasofoxifene and Abemaciclib to the Combination of Fulvestrant and Abemaciclib for the Treatment of Pre- and Postmenopausal Women and Men with Locally Advanced or Metastatic ER+/HER2 - Breast Cancer with an ESR1 Mutation.

Inclusion Criteria: 1. Pre- or postmenopausal women or men. 2. Locally advanced and/or metastatic ER+ breast cancer with radiological or clinical evidence of progression on an AI in combination with either palbociclib or ribociclib as their first hormonal treatment for metastatic disease. 3. Histological or cytological confirmation of ER+/HER2 - disease 4. No evidence of progression for at least 6 months on an AI/CDKi combination for advanced breast cancer. 5. At least 1 or more ESR1 point mutations in the ESR1 ligand binding domain as assessed in cell- free ctDNA obtained from a blood or breast cancer tissue. 6. Locally advanced or metastatic breast cancer with either measurable (according to RECIST 1.1) or non-measurable lesions. 7. Subjects may have received 1 cytotoxic chemotherapy regimen in the metastatic disease setting prior to study entry, but must have recovered from chemotherapy acute toxicity excluding alopecia and Grade 2 peripheral neuropathy. 8. Eastern Cooperative Oncology Group (ECOG) performance score of 0 or 1 9. Adequate organ function 10. Able to swallow tablets 11. Brain metastases are allowed only if the following 4 parameters hold: 1. Asymptomatic, 2. Definitively treated (e.g., radiotherapy, surgery), 3. Not requiring steroids up to 4 weeks before study treatment initiation, AND 4. Central nervous system disease stable for >3 months prior to registration as documented by magnetic resonance imagining (MRI). 12. Able to understand and voluntarily sign a written informed consent before any screening procedures. 13. Every attempt should be made to obtain a biopsy of metastatic breast cancer tissue, when safe and feasible, to provide histological or cytological confirmation of ER+/HER2- disease as assessed by a local laboratory, according to American Society of Clinical Oncology/College of American Pathologists guidelines, using slides, paraffin blocks, or paraffin samples. If a biopsy is done, it may undergo genomic testing at some point to assess for ESR1 mutations and correlation with ctDNA results. If a biopsy is not possible or inappropriate from a clinical standpoint, the ER and HER2 status from the subject's most recent biopsy must confirm that the subject is ER+ and HER2 Exclusion Criteria: 1. Lymphangitic carcinomatosis involving the lung. 2. History of Grade 3 or Grade 4 interstitial lung disease (ILD) on previous therapy. 3. Visceral crisis in need of cytotoxic chemotherapy as assessed by the investigator. 4. Prior progression of disease on abemaciclib, fulvestrant, or other selective estrogen receptor degrader (SERD) therapy. 5. Subjects with a known hypersensitivity to fulvestrant or to any of the excipients 6. Radiotherapy within 30 days prior to Visit 0 (Day 1) except in case of localized radiotherapy for analgesic purposes or for lytic lesions at risk of fracture, which can then be completed within 7 days prior to Visit 0 (Day 1). Subjects must have recovered from radiotherapy toxicities prior to Visit 0 (Day 1). 7. Known RB1 mutations or deletions that in the opinion of the investigator confer resistance to CDK4/6i. (Screening for RB1 mutation is not required for entry.) 8. History of long QTc (Q-T interval corrected for heart rate) syndrome or a QTc of >480 msec. 9. History of a pulmonary embolus (PE), deep vein thrombosis (DVT), or any known thrombophilia, unless the event occurred greater than 6 months prior to screening and the subject is treated with chronic anticoagulant therapy such as apixaban (Eliquis) or rivaroxaban (Xarelto). 10. Lasofoxifene is not recommended for use in subjects with conditions that place them at increased risk for VTEs (such as severe congestive heart failure [CHF] or prolonged immobilization). 11. On concomitant strong CYP3A4 inhibitors. 12. On strong and moderate CYP3A4 inducers. 13. Any significant co-morbidity that would impact the study or the subject's safety, including subjects with significant malabsorption. 14. Active systemic bacterial or fungal infection (requiring intravenous [IV] antibiotics or antifungals at the time of initiating study treatment). 15. Known infection with human immunodeficiency virus (HIV), hepatitis B virus (HBV), or hepatitis C virus (HCV). 16. History of malignancy within the past 5 years (excluding breast cancer), except basal cell or squamous cell carcinoma of the skin curatively treated by surgery. 17. Positive serum pregnancy test (only if premenopausal). 18. Sexually active premenopausal women and men unwilling to use double-barrier contraception. 19. Women who are breast feeding 20. History of non-compliance to medical regimens. 21. Unwilling or unable to comply with the protocol. 22. Current participation in any clinical research trial involving an investigational drug or device within the last 30 days.