-  INCLUSION CRITERIA:

          -  Clinical diagnosis of GEP-NET disease, histologically consistent with neuroendocrine
             tumor.

          -  Inoperable disease (metastatic, non-candidate for surgery with curative intent,
             locally advanced into vessels or other critical structures, etc.)

        NOTE: Presence of at least one non-irradiated index lesion (Phase II only).

          -  Patients on somatostatin analogue therapy (e.g., but not only limited to sandostatin
             or lanreotide therapy) must have initiated and been on a consistent dose of therapy
             for at least 3 months prior to study enrollment.

          -  Patients on short-term octreotide must have dose held for 24 hours without octreotide
             because this is necessary for study Lu-177-DOTATATE therapy.

          -  Age >=18 years. Because no dosing or adverse event data are currently available on the
             use of Lu-177-DOTATATE in combination with olaparib in patients <18 years of age,
             children are excluded from this study, but may be eligible for future pediatric
             trials.

          -  Must have presence of somatostatin receptors (SSTR) positive disease as documented by
             positive Ga-68-DOTATATE PET scan within 12 weeks prior to enrollment.

        NOTE: Positivity of Ga-68-DOTATATE PET scan is defined as having at least one

        RECIST 1.1 measurable lesion that has an SUV higher than or equal to liver and is
        qualitatively higher and distinguishable from background activity.

          -  Progressive disease by RECIST 1.1, as compared to previous anatomic imaging no more
             than 36 months from the date of study enrollment, with at least 1 measurable lesion by
             RECIST 1.1

          -  ECOG Performance Status of <=1

          -  Patients must have normal organ and bone marrow function measured within 28 days prior
             to enrollment as defined below:

               -  Hemoglobin >= 10.0 g/dL with no blood transfusion in the past 28 days

               -  Absolute neutrophil count (ANC) >= 1.5 x 10(9)/L

               -  Platelet count >= 100 x 10(9)/L

               -  Total bilirubin <= 1.5 x institutional upper limit of normal (ULN)

               -  Aspartate aminotransferase (AST) (Serum Glutamic Oxaloacetic Transaminase (SGOT))
                  / Alanine aminotransferase (ALT) (Serum Glutamic Pyruvate Transaminase (SGPT)) <=
                  2.5 x institutional upper limit of normal unless liver metastases are present in
                  which case they must be <= 5x ULN

               -  Patients must have creatinine clearance estimated of >= 51 mL/min using the
                  Modification of Diet in Renal Disease (MDRD) study equation or based on a 24 hour
                  urine test: eGFR = 175 x (SCr)^-1.154 x (age)^-0.203 x 0.742 [if female] x 1.212
                  [if Black]

          -  Ability to understand and willingness to sign informed consent.

          -  Postmenopausal or evidence of non-childbearing status for women of childbearing
             potential: negative urine or serum pregnancy test within 28 days of study enrollment.
             Postmenopausal is defined as:

               -  Amenorrheic for 1 year or more without an alternative medical cause; if the woman
                  received exogenous hormonal treatments, must be amenorrheic for 1 year or more
                  following cessation of the same

               -  Luteinizing hormone (LH) and Follicle stimulating hormone (FSH) levels in the
                  post-menopausal range for women under 50

               -  Radiation-induced oophorectomy with last menses >1 year ago

               -  Chemotherapy-induced menopause with >1 year interval since last menses

               -  Surgical sterilization (bilateral oophorectomy or hysterectomy)

          -  NOTE: A female is not of childbearing potential if a prior history of hysterectomy
             with bilateral oophorectomy or other procedure has rendered the patient surgically
             sterile, or >1 years since last menstruation. Must have outside
             endocrinologist/medical oncologist who can follow the patient for standard of care
             follow-ups after receiving PRRT at the NIH

          -  Pre-clinical data indicate that the study drugs can have adverse effects on
             embryofetal survival and development. It is further not known whether olaparib or its
             metabolites are found in seminal fluid. For these reasons:

               -  Women of childbearing potential and their partners, who are sexually active, must
                  agree to the use of 2 highly effective forms of contraception in combination
                  (male condom plus one of the methods listed below) or must totally/truly abstain
                  from any form of sexual intercourse. This should be started from the signing of
                  the informed consent, throughout their participation in the study and for at
                  least 7 month after the last dose of the study drugs.

               -  Male patients must use a condom during treatment and for 4 months after the last
                  dose of study drugs when having sexual intercourse with a pregnant woman or with
                  a woman of childbearing potential. Female partners of male patients should also
                  use a highly effective form of contraception (see below) if they are of
                  childbearing potential. Male patients should not donate sperm throughout the
                  period of taking olaparib and for 4 months following the last dose of the study
                  drugs.

               -  Acceptable birth control methods include:

                    -  Total sexual abstinence i.e., refrain from any form of sexual intercourse in
                       line with the patients usual and/or preferred lifestyle. Abstinence must be
                       for the total duration of the study treatment and for at least 7 month (for
                       female patients) or 4 months (for male patients) after the last dose of
                       study treatment. Periodic abstinence (e.g., calendar ovulation,
                       symptothermal, post-ovulation methods) and withdrawal are not acceptable
                       methods of contraception. Vasectomised sexual partner PLUS male condom. With
                       participant assurance that partner received post-vasectomy confirmation of
                       azoospermia.

                    -  Tubal occlusion PLUS male condom

                    -  Intrauterine Device PLUS male condom. Provided coils are copperbanded.

                    -  Etonogestrel implants (e.g., Implanon , Norplant ) PLUS male condom

                    -  Normal and low dose combined oral pills PLUS male condom

                    -  Hormonal shot or injection (e.g., Depo-Provera) PLUS male condom

                    -  Intrauterine system device (e.g., levonorgestrel-releasing intrauterine
                       system -Mirena(R)) PLUS male condom

                    -  Norelgestromin/ethinyl estradiol transdermal system PLUS male condom

                    -  Intravaginal device (e.g., ethinyl estradiol and etonogestrel) PLUS male
                       condom

                    -  Cerazette (desogestrel) PLUS male condom. Cerazette is currently the only
                       highly efficacious progesterone based pill.

        EXCLUSION CRITERIA:

          -  Patients who have any GEP-NET lesions that are negative by Ga-68-DOTATATE-PET imaging
             but positive by FDG-PET imaging.

          -  Because there is an unknown but potential risk for adverse events in nursing infants
             secondary to treatment of the mother with study drugs, breastfeeding should be
             discontinued if the mother is treated with study drugs.

          -  Other known co-existing malignancies except non-melanoma skin cancer and carcinoma in
             situ of the uterine cervix, unless definitively treated and proven no evidence of
             recurrence for 5 years.

          -  Patients who are receiving any other investigational agents.

          -  Patients receiving any systemic chemotherapy or radiotherapy (except for palliative
             reasons) within 4 weeks prior to study enrollment.

          -  Patients with persistent toxicities (>= CTCAE grade 2) with the exception of alopecia,
             caused by previous cancer therapy and toxicities deemed irreversible/stable expected
             to interfere with study drug administration in the opinion of the Principal
             Investigator.

          -  Patient s weight exceeding PET table tolerance (> 400 lbs).

          -  Uncontrolled inter-current illness including, but not limited to, ongoing or active
             infection, symptomatic congestive heart failure, unstable angina pectoris,
             hypertension (>180/110), arrhythmia, or psychiatric illness/social situations that
             would limit compliance with study requirements.

          -  Patients with symptomatic, uncontrolled brain metastases. NOTE: Patients with
             previously treated brain metastases are eligible if asymptomatic and may be on a
             stable dose of corticosteroids as long as these were started at least 4 weeks prior to
             treatment .

          -  Patients with spinal cord compression unless considered to have received definitive
             treatment for this and evidence of clinically stable disease by imaging and clinical
             assessment as assessed by the treating investigator for 28 days before enrollment.

          -  Concomitant use of known strong or moderate CYP3A inhibitors within 2 weeks before
             enrollment.

          -  Concomitant use of known strong or moderate CYP3A inducers within 5 weeks (for
             enzalutamide or phenobarbital) and 3 weeks for other agents before enrollment.

          -  Patients that have had major surgery within 4 weeks prior to study enrollment and have
             not recovered from any effects of any major surgery.

          -  Patients unable to swallow orally administered medication and patients with
             gastrointestinal disorders likely to interfere with absorption of the study
             medication.

          -  Previous allogeneic hematopoietic stem cell transplant, allogeneic bone marrow
             transplant or double umbilical cord blood transplant (duCBT).

          -  Patients with a known hypersensitivity to olaparib or Lutathera or any excipients of
             these products.

          -  Resting ECG indicating uncontrolled cardiac conditions, as judged by the investigator
             (e.g., unstable ischemia, uncontrolled symptomatic arrhythmia, congestive heart
             failure, QTcF prolongation >500 ms, electrolyte disturbances, etc.), or patients with
             congenital long QT syndrome.

          -  Patients with myelodysplastic syndrome/acute myeloid leukemia or with features
             suggestive of MDS/AML.

          -  Immunocompromised patients, e.g., patients who are known to be serologically positive
             for human immunodeficiency virus (HIV). HIV-positive patients on combination
             antiretroviral therapy are ineligible because of the potential for pharmacokinetic
             interactions with study drugs. In addition, these patients are at increased risk of
             lethal infections when treated with marrow-suppressive therapy. Appropriate studies
             will be undertaken in patients receiving combination antiretroviral therapy when
             indicated.

          -  Patients with known active hepatitis (i.e., Hepatitis B or C).

          -  Any previous treatment with PARP inhibitor, including olaparib and/or any previous
             treatment with any systemic radionuclide agents.

          -  Involvement in the planning and/or conduct of the study.

          -  Previous treatment with Lu-177-DOTATATE