Inclusion Criteria:

          1. Patients ≥18 years of age. Patients must agree to use one highly effective (less than
             1% failure rate) method of contraception or use a combination of two effective methods
             of contraception during treatment with study drug and for at least 12 weeks following
             the last dose of study drug.

          2. Have a diagnosis of metastatic TNBC previously treated with standard anthracycline,
             cyclophosphamide, and taxane chemotherapy, unless there was a contraindication to
             doxorubicin, in which case prior treatment with this agent is not required. NOTE: TNBC
             defined as ER-negative tumors with ≤10% tumor nuclei immunoreactivity, or "ER Low
             Positive" as defined by the updated ASCO/CAP guidelines 2020.

          3. Have not received more than 3 prior chemotherapy regimens for metastatic disease.
             Prior platinum and/or taxane therapy in the adjuvant or metastatic setting is
             permitted.

          4. Have locoregional (eg, breast, chest wall, regional lymphatic) or pulmonary or hepatic
             metastatic disease that is amenable to core needle biopsy. If a research biopsy from a
             patient's metastatic disease cannot be safely obtained, a skin biopsy is permitted. If
             a skin biopsy cannot be safely obtained, patients may still be eligible, per physician
             discretion.

          5. Have an Eastern Cooperative Oncology Group (ECOG) performance status of 0-2

          6. Have adequate hematologic function, defined by:

               1. Absolute neutrophil count (ANC) >1500/mm^3

               2. Platelet count ≥100,000/mm^3

               3. Hemoglobin ≥9 g/dL

          7. Have adequate liver function, defined by:

               1. AST and ALT ≤2.5 x the upper limit of normal (ULN) or ≤5 x ULN in presence of
                  liver metastases

               2. Total bilirubin ≤1.5 x ULN

          8. Have adequate renal function, defined by:

             a. Serum creatinine ≤1.5 x ULN or calculated creatinine clearance of ≥60 ml/min

          9. Have the ability to swallow oral medications

         10. Patients who have a history of brain metastasis are eligible for the study provided
             that all the following criteria are met:

               1. Brain metastases which have been treated

               2. Off-treatment with steroids for 2 weeks before administration of the first dose
                  of LY3023414 and prexasertib

               3. No ongoing requirement for dexamethasone or anti-epileptic drugs

               4. No clinical or radiological evidence of progression of brain metastases

         11. Patient must be accessible for treatment and follow-up.

         12. All patients must be able to understand the investigational nature of the study and
             give written informed consent prior to study entry.

        Exclusion Criteria:

          1. Have a family history of long QT Syndrome and serious cardiac conditions.

          2. Have QTcF interval of >470 msec on screening electrocardiogram (ECG) as well as on
             pre-dose Cycle 1 Day 1 ECG

          3. Have insulin-dependent diabetes mellitus. Patients with a type 2 diabetes mellitus are
             eligible if adequate control of blood glucose level is obtained by oral anti-diabetics
             as documented by HbA1c <8%. Patients with type 1 diabetes mellitus are not eligible.

          4. Previous radiotherapy for metastatic disease completed <2 weeks prior to study
             treatment initiation.

          5. Women who are pregnant or lactating.

          6. Patients who have any severe and/or uncontrolled medical conditions or other
             conditions that could affect their participation such as:

               1. severe impaired lung functions as defined as spirometry and DLCO that is 50% of
                  the normal predicted value and/or O2 saturation that is 88% or less at rest on
                  room air

               2. liver disease such as cirrhosis or severe hepatic impairment (Child-Pugh class
                  C).

               3. viral hepatitis or HIV.

          7. Concurrent use of CYP3A4 inhibitors and inducers from 72 hours prior to initiation of
             study treatment until the end of treatment.

          8. History of any other disease, physical examination finding, or clinical laboratory
             finding giving reasonable suspicion of a disease or condition that contraindicates use
             of an investigational drug, or that might affect interpretation of the results of this
             study, or render the patient at high risk for treatment complications.

          9. Patients who have received prior PI3K or CHK therapy.

         10. Any other investigational or anti-cancer treatments while participating in this study

         11. Any other active malignancy.