Inclusion Criteria:

          -  Histologically confirmed prostate cancer

          -  Signed informed consent form (ICF) indicating that the subject understands the purpose
             of, and procedures required for, the study and is willing to participate in the study

          -  Consent to MD Anderson laboratory protocol Lab02-152

          -  Available tumor tissue sample (recently collected +/- archival)

          -  Biochemically recurrent prostate cancer following definitive treatment with radical
             prostatectomy or / and external beam radiation therapy. Patient may have received
             prior androgen deprivation with or without other treatments in the neoadjuvant,
             adjuvant or salvage setting as long as >= 6 months from discontinuation have elapsed
             at the time of randomization

          -  Progression based on the following criteria:

               -  PSA progression: For patients with prior radical prostatectomy (+/- radiation),
                  PSA progression defined by a minimum of two rising PSA levels with an interval of
                  at least 1 week between each determination and a PSA of >= 0.5 ng/ml at
                  screening. For patients with only prior definitive radiation of the prostate, PSA
                  recurrence is defined as PSA >= nadir+2 ng/mL

               -  PSA doubling time of =< 12 months at the time of study entry. Calculation of PSA
                  doubling time should include the use of all available PSA values obtained within
                  past 12 months prior to randomization, with a minimum of 3 values >= 0.1 ng/mL
                  PSA values obtained prior to localized therapy will be excluded. PSA doubling
                  time to be estimated using Memorial Sloan Kettering Cancer Center online
                  calculator

               -  Identification of up to 5 metastatic lesions or/and pelvic node recurrent sites
                  by advanced imaging technology (PSMA PET/CT or fluciclovine PET/CT). In case of
                  inconsistency between the two imaging modalities, up to 5 lesions in the PSMA/PET
                  will be accepted. All sites should be eligible to be treated with definitive
                  intent. At least one of these lesions will be histologically confirmed.
                  Symptomatic metastatic disease or disease impending symptoms (e.g. brain
                  metastasis, painful bone metastasis, and spine disease) can be treated with
                  definitive local therapy prior to enrollment. This lesion will be counted towards
                  the total number of metastatic lesions

          -  Must be able to receive luteinizing hormone-releasing hormone (LHRH) agonist or
             antagonist during the course of the study

          -  Eastern Cooperative Oncology Group performance status (ECOG PS) of 0-1

          -  Must be able to swallow tablets

          -  To avoid risk of drug exposure through the ejaculate (even men with vasectomies),
             patients must agree while on study drug and for 3 months following the last dose of
             study drug to:

               -  Use a condom during sexual activity

               -  Not donate sperm

          -  Absolute neutrophil count (ANC) >= 1.0 x 10^9/L

          -  Hemoglobin >= 9.0 g/dL

          -  Platelet count >= 75 x 10^9/L

          -  Serum albumin >= 3 g/dL

          -  Calculated creatinine clearance >= 40 mL/min using the Cockcroft-Gault equation

          -  Serum total bilirubin =<1.5 x upper limit of normal (ULN) or direct bilirubin =< 1.5 x
             ULN (Note: in subjects with Gilbert's syndrome, if total bilirubin is > 1.5 x ULN,
             measure direct and indirect bilirubin, and if direct bilirubin is =< 1.5 x ULN,
             subject may be eligible)

          -  Aspartate aminotransferase (AST) or alanine aminotransferase (ALT) =< 3.0 x ULN

          -  Testosterone > 150 ng/dL. For patients treated with ADT with or without short-term
             first generation anti androgens (e.g. bicalutamide) up to 4 weeks prior to
             randomization, a testosterone measurement prior to the ADT treatment will be used to
             determine eligibility, and must have been > 150 ng/dL. If no testosterone level is
             available from before luteinizing hormone-releasing hormone analogue (LHRHa) injection
             and within 6 weeks of randomization, the patient will be ineligible

        Exclusion Criteria:

          -  Histologically confirmed recurrence in a prior definitively irradiated prostate cancer
             field per the judgment of the investigator

          -  Ongoing androgen deprivation therapy (with or without short-term first generation
             anti-androgens) for > 4 weeks at the time of randomization

          -  =< 30 days prior to cycle 1 day 1, patient had:

               -  A transfusion (platelets or red blood cells)

               -  Hematopoietic growth factors

               -  An investigational agent (=< 30 days or 5 half-lives, whichever is longer)

               -  Major surgery

          -  Active hematologic or solid malignancy other than prostate cancer with at least 30%
             chance of recurrence per investigator assessment; (exceptions: adequately treated
             basal cell or squamous cell skin cancer, superficial bladder cancer, or any other
             cancer in situ currently in complete remission)

          -  Known allergies, hypersensitivity, or intolerance to apalutamide or LHRH
             agonist/antagonist or excipients

          -  Current evidence of any of the following:

               -  Uncontrolled hypertension

               -  Gastrointestinal disorder affecting absorption

          -  Corrected QT interval by the Fridericia correction formula (QTcF) > 450 msec on the
             screening electrocardiogram (ECG)

          -  History of clinically significant cardiovascular disease including, but not limited
             to:

               -  Myocardial infarction or unstable angina =< 3 months prior to treatment
                  initiation

               -  Clinically significant cardiac arrhythmia

               -  Pulmonary embolism, stroke =< 3 months prior to treatment initiation

               -  Congestive heart failure (New York Heart Association class III-IV)

          -  Known evidence of an active infection requiring systemic therapy such as human
             immunodeficiency virus (HIV), active hepatitis, or fungal infection

          -  History of seizure disorder

          -  Patients receiving medications known to lower the seizure unless discontinued or
             substituted at least 4 weeks prior to study entry. These medications include:

               -  Aminophylline/theophylline,

               -  Atypical antipsychotics (e.g., clozapine, olanzapine, risperidone, ziprasidone),

               -  Bupropion,

               -  Lithium,

               -  Meperidine and pethidine,

               -  Phenothiazine antipsychotics (e.g., chlorpromazine, mesoridazine, thioridazine),

               -  Tricyclic and tetracyclic antidepressants (e.g., amitriptyline, desipramine,
                  doxepin, imipramine, maprotiline, mirtazapine)

          -  Any contraindication that precludes use or radiotherapy for identified lesion
             treatment per the judgment of the investigator

          -  Any condition for which, in the opinion of the investigator, participation would not
             in the best interest of the subject (e.g., compromise the well-being) or that could
             prevent, limit, or confound the protocol-specified assessments