This phase I trial studies the side effects and best dose of olaparib when given together with high-dose chemotherapy in treating patients with lymphomas that have come back or does not treatment and are undergoing stem cell transplant. Drugs used in chemotherapy, such as olaparib, vorinostat, gemcitabine, busulfan, and melphalan, work in different ways to stop the growth of cancer cells, either by killing the cells, by stopping them from dividing, or by stopping them from spreading. Immunotherapy with monoclonal antibodies, such as rituximab, may help the body's immune system attack the cancer, and may interfere with the ability of tumor cells to grow and spread. Giving olaparib and high-dose chemotherapy together may work better in treating patients with relapsed/refractory lymphomas undergoing stem cell transplant than with chemotherapy alone.

PRIMARY OBJECTIVE:

I. Establish the maximum tolerated dose (MTD) of olaparib combined with vorinostat/gemcitabine/busulfan/melphalan with autologous stem-cell transplant [ASCT]).

SECONDARY OBJECTIVES:

I. Determine the 2-year event-free survival (EFS). II. 2-year overall survival (OS). III. Complete remission (CR) rate. IV. Overall remission rate (ORR). V. Describe the toxicity profile. VI. Describe changes of deoxyribonucleic acid (DNA) damage response and repair, poly(ADP-ribose) polymerase (PARP) inhibition and downstream cellular effects in peripheral blood mononuclear cells and, when available, malignant lymphocytes obtained by fine needle aspiration (FNA) of peripheral lymph nodes.

OUTLINE: This is a dose-escalation study of olaparib.

Patients receive olaparib orally (PO) twice daily (BID) on days -11 to -3, vorinostat PO on days -10 to -3, gemcitabine intravenously (IV) over 4.5 hours on days -9 and -4, busulfan IV over 3 hours on day -9 to -6, melphalan IV over 30 minutes on days -4 and -3, and undergo peripheral blood stem cell transplant IV over 30-60 minutes on day 0. Patients with CD20+ tumors also receive rituximab IV over 3-6 hours on day -10.

After completion of study treatment, patients are followed up every 1-2 days for 30 days and then every 2 weeks for up to 100 days.

Inclusion Criteria:

1. Age 18-65

2. Patients with:

   2.1 Diffuse large B-cell lymphoma (DLBCL) with one of the following: 2.1.1 Primary refractory (no CR to 1st line) 2.1.2 High-risk relapse, defined as any of the following: CR1 <6 mo, secondary IPI >1, or LDH > 225 U/L. 2.1.3 Refractory relapse: No response to >/= 1 salvage line and not eligible to receive other novel salvage therapies, such as CAR-T in a timely fashion or have already failed these.

   2.2 Hodgkin's with one of the following: 2.2.1 Primary refractory (no CR or PD within 3 months) 2.2.2 High-risk relapse, defined as any of the following: CR1 <1 year, extranodal relapse, or B symptoms.

   2.2.3 Refractory relapse: No response to >/= 1 salvage line 2.3 T-non Hodgkin's lymphoma (T-NHL) with one of the following: 2.3.1 Primary refractory (no CR to 1st line) 2.3.2 High-risk relapse (within 6 months) 2.3.3 Refractory relapse to >/= 1 line of salvage 2.3.4 Any other lymphoma that is refractory or relapsed and that does not qualify for autologous transplant protocols of higher priority.

3. Adequate renal function (creatinine clearance estimated using the Cockcroft-Gault equation of >/= 51 mL/min: Estimated creatinine clearance = (140-age [years]) x weight (kg) (xF)a / serum creatinine (mg/dL) x 72 [a where F=0.85 for females and F=1 for males.]

4. Adequate hepatic function (Aspartate aminotransferase (AST) (Serum Glutamic Oxaloacetic Transaminase (SGOT)) / Alanine aminotransferase (ALT) (Serum Glutamic Pyruvate Transaminase (SGPT)) </= 3.5 x institutional upper limit of normal unless liver metastases or a systemic inflammatory picture secondary to the lymphoma are present in which case they must be </= 6x ULN; total bilirubin </= 2.5 x ULN or </= 3.5 x ULN if Gilbert's disease)

5. Prothrombin time (PT) </=1.5 x institutional upper limit of normal

6. Adequate pulmonary function (FEV1, FVC and DLCOc >/= 50% of predicted)

7. Adequate cardiac function (LVEF >/= 40%, no uncontrolled arrhythmias or symptomatic cardiac disease

8. ECOG performance status <2

9. Provision of informed consent prior to any study specific procedures

10. Patients must have a life expectancy >/= 16 weeks

11. Postmenopausal or evidence of non-childbearing status for women of childbearing potential: negative urine or serum pregnancy test within 28 days and within 72 hours of study treatment and confirmed prior to receiving treatment on this study. Patients with positive results will be removed from the study. Postmenopausal is defined as one of the following:

    11.1 Amenorrheic for 1 year or more following cessation of exogenous hormonal treatments.

    11.2 Luteinizing hormone (LH) and Follicle stimulating hormone (FSH) levels in the postmenopausal range for women under 50.

    11.3 Radiation-induced oophorectomy with last menses >1 year ago. 11.4 Chemotherapy-induced menopause with >1 year interval since last menses. 11.5 Surgical sterilization (bilateral oophorectomy or hysterectomy). 11.6 Female patients must agree to use a highly effective birth control method while on study and for at least 6 months after the last dose of study drug(s).

12. Male patients and their partners, who are sexually active and of childbearing potential, must agree to the use of two highly effective forms of contraception in combination, throughout the period of taking study treatment and for 6 months after last dose of study drug(s) to prevent pregnancy in a partner.

13. Patient is willing and able to comply with the protocol for the duration of the study including undergoing treatment and scheduled visits and examinations.

14. Prior apheresis of >/= 3 million CD34+ cells/Kg.

Eligibility for ASCT is determined by the above inclusion criteria 3-7.

Exclusion Criteria:

1. Persistent toxicities (>Common Terminology Criteria for Adverse Event (CTCAE) grade 2) caused by previous cancer therapy, excluding alopecia.
2. Prior whole brain irradiation
3. Active hepatitis B, either active carrier (HBsAg +) or viremic (HBV DNA >/= 10,000 copies/mL, or >/= 2,000 IU/mL)
4. Evidence of either cirrhosis or stage 3-4 liver fibrosis in patients with chronic hepatitis C or positive hepatitis C serology
5. Active infection requiring parenteral antibiotics
6. Patients who are known to be serologically positive for human immunodeficiency virus (HIV).
7. Patients receiving any systemic chemotherapy or radiotherapy (except for palliative reasons) within 3 weeks prior to study treatment
8. Pregnancy
9. Other malignancy within the last 5 years except: adequately treated non-melanoma skin cancer, curatively treated in situ cancer of the cervix, ductal carcinoma in situ (DCIS), Stage 1, grade 1 endometrial carcinoma, or other solid tumors.
10. Resting ECG with QTcF > 470 msec on 2 or more time points within a 24 hour period or family history of long QT syndrome.
11. Concomitant use of known strong CYP3A inhibitors (eg. itraconazole, telithromycin, clarithromycin, protease inhibitors boosted with ritonavir or cobicistat, indinavir, saquinavir, nelfinavir, boceprevir, telaprevir) or moderate CYP3A inhibitors (eg. ciprofloxacin, erythromycin, diltiazem, fluconazole, verapamil). The required washout period prior to starting olaparib is 2 weeks.
12. Concomitant use of known strong (eg. phenobarbital, enzalutamide, phenytoin, rifampicin, rifabutin, rifapentine, carbamazepine, nevirapine and St John's Wort ) or moderate CYP3A inducers (eg. bosentan, efavirenz, modafinil). The required washout period prior to starting olaparib is 5 weeks for enzalutamide or phenobarbital and 3 weeks for other agents.
13. Patients with myelodysplastic syndrome/acute myeloid leukaemia or with features suggestive of MDS/AML.
14. Patients with symptomatic uncontrolled brain metastases. A scan to confirm the absence of brain metastases is not required. The patient can receive a stable dose of corticosteroids before and during the study 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 for 28 days.
15. Major surgery within 2 weeks of starting study treatment and patients must have recovered from any effects of any major surgery.
16. Uncontrolled non-malignant systemic disease or active, uncontrolled infection. Examples include, but are not limited to, uncontrolled ventricular arrhythmia, recent (within 3 months) myocardial infarction, uncontrolled major seizure disorder, unstable spinal cord compression, superior vena cava syndrome, extensive interstitial bilateral lung disease on High Resolution Computed Tomography (HRCT) scan or any psychiatric disorder that prohibits obtaining informed consent.
17. Patients unable to swallow orally administered medication and patients with gastrointestinal disorders likely to interfere with absorption of the study medication.
18. Breast feeding women.
19. Patients with a known hypersensitivity to olaparib or any of the excipients of the product.
20. Medical, psychiatric, cognitive or other conditions that compromise the patient's ability to understand the patient information, to give informed consent, to comply with the study protocol or to complete the study.