Phase Ib Study of Stereotactic Body Radiotherapy (SBRT) in Oligometastatic Non-small Lung Cancer (NSCLC) With Dual Immune Checkpoint Inhibition

Inclusion Criteria: * Participants with histologically or cytologically confirmed stage IV NSCLC not amenable to curative surgery or radiation * Participants may have had prior chemotherapy or be chemotherapy naïve * Participants must have tumors that lack sensitizing EGFR mutation (e.g. exon 19 deletion or exon 21 L858R) or ALK rearrangement. If a participant has squamous histology, then EGFR and ALK testing is not required. * No prior treatment with cancer immunotherapy including, but not limited to, other anti-CTLA-4, anti-PD-1, anti-PD-L1, and anti-programmed cell death ligand 2 anti- (PD-L2) antibodies, excluding therapeutic anticancer vaccines. * Participants will have 6 or less extracranial sites, which can safely receive SBRT between 30 - 50 Gy in 5 fractions. A site may have multiple tumor lesions within it as long as the gross tumor volume (GTV) of the site is 8 cm or less and can be covered in an acceptable SBRT field determined by the PI. All gross disease must be amenable to treatment with SBRT, as allowable per normal tissue constraints. Participants will not have had any prior radiation therapy significantly overlapping a tumor site to be treated. * Participants must have evaluable disease, as defined by RECIST 1.1. * World Health Organization (WHO)/Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1 at enrollment * Life expectancy of \> 12 weeks * Participant is willing and able to comply with the protocol for the duration of the study including undergoing treatment and scheduled visits and examinations including follow up. * Participants with treated metastatic lesions to the brain may be enrolled after completing stereotactic radiosurgery (may enroll 14 days after treatment) or whole brain radiation (may enroll 14 days after treatment) and must be off corticosteroids for 14 days prior to start of SBRT. * Adequate normal organ and marrow function as defined below: * Hemoglobin ≥ 9.0 g/dL * Absolute neutrophil count (ANC) ≥ 1.5 x 10\^9/L (\> 1500 per mm\^3) * Platelet count ≥ 100 x 10\^9/L (\>100,000 per mm\^3) * Serum bilirubin ≤ 1.5 x institutional upper limit of normal (ULN). This will not apply for participants with confirmed Gilbert's syndrome, who will be allowed in consultation with their physician. * AST (SGOT)/ALT (SGPT) ≤ 2.5 x ULN unless liver metastases are present, in which case ALT and AST must be ≤ 5x ULN * Serum creatinine \<1.5 x upper limit of normal (ULN) OR creatinine clearance (CrCl) ≥30 mL/min for participants with creatinine levels \>1.5 × institutional ULN * Female participant of childbearing potential should have a negative urine or serum pregnancy prior to receiving the first study treatment. If the urine test is positive or cannot be confirmed as negative, a serum pregnancy test will be required * Female participants of childbearing potential should be willing to use 1 method of highly effective birth control, 2 methods of effective birth control, be surgically sterile, or abstain from heterosexual activity for the course of the study through 180 days after the last dose of study medication. Participants of childbearing potential are those who have not been surgically sterilized or have not been free from menses for \> 1 year. * Evidence of post-menopausal status or negative urinary or serum pregnancy test for female pre-menopausal patients. Women will be considered post-menopausal if they have been amenorrheic for 12 months without an alternative medical cause. The following age-specific requirements apply: * Women \< 50 years of age would be considered post-menopausal if they have been amenorrheic for 12 months or more following cessation of exogenous hormonal treatments and if they have luteinizing hormone and follicle- stimulating hormone levels in the post-menopausal range for the institution or underwent surgical sterilization (bilateral oophorectomy or hysterectomy). * Women ≥ 50 years of age would be considered post-menopausal if they have been amenorrheic for 12 months or more following cessation of all exogenous hormonal treatments, had radiation-induced oophorectomy with last menses \>1 year ago, had chemotherapy-induced menopause with \> 1 year interval since last menses, or underwent surgical sterilization (bilateral oophorectomy or hysterectomy). * Participant must be willing and able to provide written informed consent for the trial. Exclusion Criteria: * Involvement in the planning and/or conduct of the study (applies to both AstraZeneca staff and/or staff at the study site) * Previous enrollment in the present study * Mixed small-cell lung cancer and sarcomatoid variant NSCLC histology * Any concurrent chemotherapy, IP, biologic, or hormonal therapy for cancer treatment. Concurrent use of hormonal therapy for non-cancer-related conditions (eg, hormone replacement therapy) is acceptable. * Major surgical procedure (as defined by the Investigator) within 14 days prior to the start of study treatment. * Participants with untreated spinal cord compression. Participants with spinal cord compression may be enrolled if stable after completing surgery (may enroll 14 days after surgery) or radiation (may enroll 14 days after radiation) and must be off corticosteroids for at least 14 days prior to the start of SBRT. * Participants with untreated brain metastasis. Participants with metastatic lesions to the brain may be enrolled after completing stereotactic radiosurgery or whole brain radiation (may enroll 14 days after radiation and must be off corticosteroids for at least 14 days prior to the start of SBRT. * Any previous treatment with a PD1 or PD-L1 inhibitor, including durvalumab or an anti-CTLA4 inhibitor including tremelimumab * Participants with a known targetable EGFR mutation or ALK rearrangement * History of another primary malignancy except for: * Malignancy treated with curative intent and with no known active disease ≥2 years * Non-metastatic prostate adenocarcinoma, or treated superficial non-invasive bladder cancer * Adequately treated carcinoma in situ without evidence of disease (eg, cervical cancer in situ) * Adequately treated non-melanoma skin cancer or lentigo maligna without evidence of disease * Receipt of the last dose of anti-cancer therapy (chemotherapy, immunotherapy, endocrine therapy, targeted therapy, biologic therapy, tumor embolization, monoclonal antibodies, other investigational agent) ≤ 14 days of registration * Mean QT interval corrected for heart rate using Fridericia's formula (QTcF) ≥470 ms. Abnormality must be confirmed on 3 ECGs. * Current or prior use of immunosuppressive medication within 14 days before the first dose of durvalumab or tremelimumab The following are exceptions to this criterion: * Intranasal, inhaled, topical steroids, or local steroid injections (eg, intra-articular injection). * Systemic corticosteroids at physiologic doses not to exceed 10 mg/day of prednisone or its equivalent * Steroids as premedication for hypersensitivity reactions (eg, CT scan premedication) * Active or known autoimmune disease that has required immunosuppressive systemic treatment in past 2 years (ie, with use of disease modifying agents, corticosteroids, or immunosuppressive drugs). Replacement therapy (eg, thyroxine, insulin, or physiologic corticosteroid replacement therapy for adrenal or pituitary insufficiency) is not considered a form of systemic treatment and is allowed. The following are exceptions to this criterion: * Participants with vitiligo or alopecia, * Grave's disease, * Hypothyroidism (eg, following Hashimoto syndrome), * Psoriasis not requiring systemic treatment (within the past 2 years) * Participants with celiac disease controlled by diet alone * History of active primary immunodeficiency * History of allogeneic organ transplant * Active infection, including tuberculosis (clinical evaluation), hepatitis B, hepatitis C, or human immunodeficiency virus (HIV, positive HIV 1 or 2 antibodies). Active hepatitis B virus (HBV) is defined by a known positive HBV surface antigen (HBsAg) result. Participants with a past or resolved HBV infection (defined as the presence of hepatitis B core antibody and absence of HBsAg) are eligible. Participants positive for hepatitis C virus (HCV) antibody are eligible only if polymerase chain reaction is negative for HCV ribonucleic acid (RNA). * History of leptomeningeal carcinomatosis * Receipt of live attenuated vaccination within 30 days prior to the first dose of IP. Note: Participants, if enrolled, should not receive live vaccine during the study and up to 30 days after the last dose of IP. * Any condition or uncontrolled intercurrent illness that, in the opinion of the Investigator, would interfere with the evaluation of IP or interpretation of patient safety or study results, including, but not limited to, ongoing or active infection, symptomatic congestive heart failure, uncontrolled hypertension, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirement, substantially increase risk of incurring AEs from durvalumab or tremelimumab, or compromise the ability of the patient to give written informed consent * Subjects with uncontrolled seizures. * Female participants who are pregnant or breast-feeding or male or female patients of reproductive potential who are not willing to employ effective birth control from screening to 180 days after the last dose of durvalumab and tremelimumab combination therapy or 90 days after the last dose of durvalumab monotherapy. * History of hypersensitivity to IP or comparator agents * History of medically diagnosed pneumonitis or interstitial lung disease