Biologically Guided Radiation Therapy (BgRT) and Stereotactic Body Radiation Therapy (SBRT) With Osimertinib for the Treatment of Patients With Oligoprogressive EGFR Positive Non-small Cell Lung Carcinoma

Inclusion Criteria: Documented informed consent of the participant and/or legally authorized representative Assent, when appropriate, will be obtained per institutional guidelines Age: >= 18 years Eastern Cooperative Oncology Group (ECOG) =< 2 Histologically confirmed advanced non-small cell lung cancer (NSCLC) The tumor harbors 1 of the 2 common epidermal growth factor receptor (EGFR) mutations known to be associated with epidermal growth factor receptor tyrosine kinase inhibitors (EGFR-TKI) sensitivity (Ex19del or L858R), either alone or in combination with other epidermal growth factor receptor (EGFR) mutations, which may include T790M. Disease progression in the metastatic setting on PET or CT imaging when receiving first line standard/approved single agent osimertinib after having had stable disease (per Response Evaluation Criteria in Solid Tumors [RECIST] version [v] 1.1 or PET Response Criteria in Solid Tumors [PERCIST] v 1.0) for more than 6 months Disease progression must be in the form of 1-5 extracranial sites (any number of metastatic sites at initial diagnosis will qualify). For progression of the primary and oligoprogressive site(s), the primary should be treated with curative/local control intent. The primary, if progressing is considered as 1 site. Maximum of 3 lesions per organ (i.e. patient with 4 oligoprogressive sites in the lung would be excluded). Each lesion will be considered as 1 "site" so 3 lesions in the lung for example will be considered 3 sites. Patients with prior metastases that have been treated with ablative therapies before their current line of systemic therapy are eligible. Patients with brain metastases can be included but brain metastases must be treated (asymptomatic and have had no requirement for steroid medication for 1 week prior to the first dose of study drug and have completed radiation 2 weeks prior to the first dose of study drug) prior to enrollment (brain metastases [mets] will not be counted as a site of progression) Lesion(s) must be amenable to SBRT as determined by the radiation oncologist. If a patient is unable to receive a minimum of 30 Gy in 5 fractions they will not qualify At least one lesion must be amenable to BgRT which includes either a lung or bone metastasis, greater than or equal to 2 cm, which can also receive a minimum of 30 Gy in 5 fractions No prior systemic therapy for advanced disease other than osimertinib Women of childbearing potential (WOCBP): negative urine or serum pregnancy test If the urine test is positive or cannot be confirmed as negative, a serum pregnancy test will be required Agreement by females and males of childbearing potential* to use an effective method of birth control or abstain from heterosexual activity for the course of the study through at least 4 months after the last dose of protocol therapy Childbearing potential defined as not being surgically sterilized (men and women) or have not been free from menses for > 1 year (women only) Patients must be able to swallow and retain oral medications Life expectancy of at least 6 months Exclusion Criteria: Chemotherapy, radiation therapy, biological therapy, immunotherapy within 21 days prior to day 1 of protocol therapy (6 weeks for nitrosoureas or mitomycin C). Exceptions to this exclusion are brain radiation (2 weeks) and osimertinib Strong CYP3A4 inducers/ inhibitors within 14 days prior to day 1 of protocol therapy Patients receiving class 1A or class III antiarrhythmic agents within 14 days prior to day 1 of protocol therapy Drugs known to prolong the corrected QT (QTc) interval History of allergic reactions attributed to compounds of similar chemical or biologic composition to study agent Clinically significant uncontrolled illness Active infection requiring antibiotics bacterial, viral, or fungal infections, requiring systemic therapy Known history of immunodeficiency virus (HIV) or hepatitis B or hepatitis C infection Prior malignancy other than carcinoma in situ of the cervix, or nonmelanoma skin cancer, unless that prior malignancy was diagnosed and definitively treated 5 or more years prior to study entry with no subsequent evidence of recurrence. Patients with a history of low grade (Gleason score =< 6 =Gleason group 1) localized prostate cancer will be eligible even if diagnosed less than 5 years prior to study entry. Other malignancies with low probability of recurrence may be allowed with primary investigator (PI) approval Females only: Pregnant or breastfeeding Any malabsorption condition Any other condition that would, in the Investigator's judgment, contraindicate the patient's participation in the clinical study due to safety concerns with clinical study procedures Diagnosis of congenital long QT syndrome New York Heart Association Class III or IV, cardiac disease, myocardial infarction within the past 6 months, unstable arrhythmia, or evidence of ischemia on electrocardiogram (ECG) Clinical evidence of central nervous system (CNS) metastases or leptomeningeal carcinomatosis, except for individuals who have previously-treated CNS metastases, are asymptomatic, and have had no requirement for steroid medication for 1 week prior to the first dose of study drug and have completed radiation 2 weeks prior to the first dose of study drug Patients with active interstitial lung disease (ILD) / pneumonitis or with a history of ILD/ pneumonitis requiring steroids Prospective participants who, in the opinion of the investigator, may not be able to comply with all study procedures (including compliance issues related to feasibility/logistics)