Apalutamide and Gonadotropin-Releasing Hormone Analog With or Without Abiraterone Acetate in Treating Participants With Prostate Cancer

Inclusion Criteria: * Patients must have histologically or cytologically confirmed adenocarcinoma of the prostate with no histological variants (such as small cell, sarcomatoid, pure ductal cancer, transitional cell carcinoma). * Patients may have received one prior depot injection of LHRH agonist or LHRH antagonist (degarelix) within 30 days prior to study entry. Patients who have received any other prior hormonal therapy or any chemotherapy for prostate cancer will be excluded. (Patients who have discontinued finasteride or dutasteride or testosterone supplement for at least 2 weeks will be allowed to enroll). * Be willing/able to adhere to the prohibitions and restrictions specified in this protocol. * Have signed an informed consent document indicating that the subject understands the purpose of and procedures required for the study and is willing to participate in the study. * Written authorization for use and release of health and research study information has been obtained. * Pathology review at Monroe Dunaway (MD) Anderson (Note: if patient's prostate biopsy was not read at MD Anderson, it must be reviewed at the study site to confirm eligibility). * Prostate biopsy. If previous biopsy has been performed within 3 months of screening, second biopsy procedure will not be required, if archival biopsies and at least one formalin fixed paraffin embedded biopsy tissue block containing tumor is available. * The following tumor stage and Gleason scores: a) clinical \>= stage T1c/T2 tumor with Gleason score \>=8 b) clinical stage \>= T2b tumor with Gleason score \>= 7 and PSA \> 10 ng/ml. * Serum testosterone \> 150 ng/dL. For patients treated up to 1 month of LHRH agonist, a testosterone measurement prior to the LHRH treatment will be used to determine eligibility, and must have been \> 150 ng/dL. If no testosterone level is available from before LHRHa injection up to 30 days prior to study entry, the patient will be ineligible. * Patient is suitable for prostatectomy. * No evidence of metastatic disease as determined by imaging procedures. * Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1. * Hemoglobin \>= 9.0 g/dL independent of transfusion. * Platelet count \>= 100,000/uL. * Absolute peripheral neutrophil count (ANC) \> 1,000. * Creatinine clearance \>= 50 mL/min. * Serum potassium \>= 3.5 mmol/L. * Serum bilirubin =\< 1.5 x upper limit of normal (ULN). * Alanine aminotransferase (ALT) and aspartate aminotransferase (AST) =\< 2.5 x ULN. * Serum albumin \>= 3 g/dl. * Able to swallow the study drug whole as a tablet. * Patients must have normal coagulation profile and no history of substantial non-iatrogenic bleeding diathesis. * Agrees to use a condom (even men with vasectomies) and another effective method of birth control if he is having sex with a woman of childbearing potential or agrees to use a condom if he is having sex with a woman who is pregnant while on study drug and for 3 months following the last dose of study drug. Must also agree not to donate sperm during the study and for 3 months after receiving the last dose of study drug. * Willing to take abiraterone acetate on an empty stomach; no food should be consumed at least two hours before and for at least one hour after the dose of abiraterone acetate is taken. * Life expectancy of greater than 12 months. Exclusion Criteria: * Patients who have had any prior chemotherapy or radiotherapy for prostate cancer. * Patients who have had \> 1 LHRH agonist or antagonist depot injection or received depot injection \> 30 days before study entry. * Patients may not be receiving any other investigational agents. * Patients may not be receiving the concomitant administration of any systemic therapy, biologic therapy, or other agents with anti-tumor activity against prostate cancer while the patients are on study. * Patients with known metastatic prostate cancer. * History of allergic reactions attributed to compounds of similar chemical or biologic composition to leuprolide acetate, abiraterone acetate, prednisone or apalutamide or other agents used in the study. * Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements. * Human immunodeficiency virus (HIV)-positive patients on combination antiretroviral therapy are ineligible because of the potential for pharmacokinetic interactions with apalutamide and abiraterone. Appropriate studies will be undertaken in patients receiving combination antiretroviral therapy when indicated. * Avoid concomitant strong CYP3A4 inducers during abiraterone acetate treatment. If a strong CYP3A4 inducer must be co-administered, increase the abiraterone acetate dosing frequency. * Avoid co-administration of abiraterone acetate with CYP2D6 substrates that have a narrow therapeutic index. If an alternative treatment cannot be used, exercise caution and consider a dose reduction of the concomitant CYP2D6 substrate. * Patients receiving medications known to lower the seizure threshold are ineligible unless discontinued or substituted at least 4 weeks prior to study entry. These include: 1) aminophylline/theophylline; 2) atypical antipsychotics (e.g., clozapine, olanzapine, risperidone, ziprasidone); 3) bupropion; 4) lithium; 5) pethidine; 6) phenothiazine antipsychotics (e.g., prochlorperazine (compazine), chlorpromazine, mesoridazine, thioridazine); 7) tricyclic and tetracyclic antidepressants (e.g., amitriptyline, desipramine, doxepin, imipramine, maprotiline, mirtazapine). * Chronically uncontrolled hypertension, defined conventionally as consistent systolic pressures above 170 or diastolic pressures above 110 despite anti-hypertensive therapy. Note that this is NOT a criterion related to particular blood pressure (BP) results at the time of assessment for eligibility, nor does it apply to acute BP excursions that are related to iatrogenic causes, acute pain or other transient, reversible causes. (for example doctor's visit related stress i.e. "white coat syndrome". * Requirement for corticosteroids greater than the equivalent of 10 mg of prednisone daily for more than 2 weeks. * Poorly controlled diabetes defined by hemoglobin A1C \> 9.0 at screening. * Active or symptomatic viral hepatitis or chronic liver disease. * Known history of pituitary or adrenal dysfunction. * Other malignancy, except non-melanoma skin cancer, that is active or has a \>= 30% probability of recurrence within 12 months. * History of gastrointestinal disorders (medical disorders or extensive surgery) which may interfere with the absorption of the study drug. * Prior hormone therapy for prostate cancer including orchiectomy, antiandrogens, ketoconazole, or estrogens (5-alpha reductase inhibitors allowed), or LHRH agonists/antagonists (Note: LHRH allowed if begun within 1 month of day 1). * Prior systemic treatment with an azole drug within four weeks of cycle 1 day 1. * Current enrollment in an investigational drug or device study or participation in such a study within 30 days of cycle 1 day 1. * Allergies, hypersensitivity, or intolerance to prednisone, LHRH analog or excipients of prednisone LHRH analog, abiraterone acetate and apalutamide. * Previous use of abiraterone acetate or other investigational CYP17 inhibitor (e.g., TAK-700). * Previous investigational antiandrogens (e.g., apalutamide, enzalutamide, BMS-641988). * Condition or situation which, in the investigator's opinion, may put the patient at significant risk, may confound the study results, or may interfere significantly with patient's participation in the study. * Patients unable to tolerate transrectal ultrasound. * Anti-androgens (steroidal or non-steroidal) such as cyproterone acetate, flutamide, nilutamide, bicalutamide, etc. other than assigned study drug unless given for =\< 4 weeks. * Estrogens, progestational agents such as megestrol, medroxyprogesterone, diethylstilbestrol (DES), cyproterone, spironolactone \> 50 mg/kg, etc. unless discontinued at least two weeks prior to randomization. * Androgens such as testosterone, dehydroepiandrosterone (DHEA), etc. unless discontinued at least two weeks prior to randomization. * Herbal products that may decrease PSA levels (e.g., saw palmetto) unless discontinued two weeks prior to randomization. * Active infection or other medical condition that would make prednisone/prednisolone (corticosteroid) use contraindicated. * Severe hepatic impairment (Child-Pugh Class C). * History of significant bleeding disorder unrelated to cancer, including: 1) diagnosed congenital bleeding disorders (e.g., von Willebrand's disease); 2) diagnosed acquired bleeding disorder within one year (e.g., acquired anti-factor VIII antibodies) of screening visit; 3) history of gastrointestinal (GI) bleeding within 3 months of screening visit requiring \>= 2 units packed red blood cells. * Clinically significant cardiovascular disease including: 1) myocardial infarction within 6 months of screening visit; 2) uncontrolled angina within 3 months of screening visit; 3) congestive heart failure New York Heart Association (NYHA) class 3 or 4, or subjects with history of congestive heart failure NYHA class 3 or 4 in the past, or history of anthracycline or anthracenedione (mitoxantrone) treatment, unless a screening echocardiogram or multi-gated acquisition scan (MUGA) performed within three months of the Screening visit results in a left ventricular ejection fraction that is \>= 50%. 4) history of clinically significant ventricular arrhythmias (e.g., ventricular tachycardia, ventricular fibrillation, torsade de pointes). 5) prolonged corrected QT interval by the Fridericia correction formula (QTcF) on the screening electrocardiogram (ECG) \> 470 msec. 6) history of Mobitz II second degree or third degree heart block without a permanent pacemaker in place. 7) hypotension (systolic blood pressure \< 86 mmHg or bradycardia with a heart rate of \< 50 beats per minute on the screening ECG, unless pharmaceutically induced and thus reversible (i.e. beta blockers).