Bintrafusp Alfa With Chemotherapy for Tyrosine Kinase Inhibitor-Resistant EGFR-Mutant Non-small Cell Lung Cancer

Inclusion Criteria:

* Age equal or greater than 18 years old and willing to give their signed consent
* Histologically or cytologically confirmed non-squamous, non-small cell lung cancer
* Locally advanced or metastatic disease, not amenable to curative surgery or radiotherapy
* Patients must have one of the following:

  * NSCLC which harbors EGFR Exon 19 deletion.
  * NSCLC which harbors EGFR L858R mutation.
  * NSCLC which harbors EGFR G719X, S768X, L861X mutation, and other activating uncommon mutations in exon 18-21
  * NSCLC which harbors EGFR exon20 insertion
  * NSCLC which harbors EGFR T790M mutation EGFR deletion/mutation must be documented by a Clinical Laboratory Improvement Amendments (CLIA) certified test
* Eastern Cooperative Oncology Group (ECOG) performance status 0-1
* At least one target lesion, not previously irradiated and not chosen for biopsy during the study screening period, that can be accurately measured at baseline at equal or greater than 10 mm in the longest dimension by Response Evaluation Criteria in Solid Tumors (RECIST) 1.1
* Patients must have received at least one line of EGFR tyrosine kinase inhibitor (TKI) treatment, if an Food and Drug Administration (FDA)-approved treatment exist for the EGFR mutation. Patients whose tumor harboring EGFR T790M mutation must have received prior osimertinib (or another EGFR TKI with demonstrated activity against T790M mutation). Patients who received more than one EGFR TKIs are eligible. Up to two lines of TKIs are allowed
* Absolute neutrophil count (ANC) \>= 1,500/mm\^3 (obtained less than 4 weeks from study entry)
* Platelet count \>= 100,000/mm\^3 (obtained less than 4 weeks from study entry)
* Hemoglobin (HgB) \>= 9 g/dL (obtained less than 4 weeks from study entry)
* Creatinine =\< 1.5 x upper limit of normal (ULN) (obtained less than 4 weeks from study entry)
* International normalized ratio (INR) =\< 1.5 and partial thromboplastin time (PTT) (PTT/activated partial thromboplastin time \[aPTT\]) \< 1.5 x upper limits of normal (ULN) (obtained less than 4 weeks from study entry). Patients receiving warfarin must be switched to low molecular weight heparin and have achieved stable coagulation profile prior to first dose of protocol therapy
* Total serum bilirubin =\< 1.5 x ULN (patients with known Gilbert Syndrome, a total bilirubin =\< 3.0 x ULN, with direct bilirubin =\< 1.5 x ULN) (obtained less than 4 weeks from study entry)
* Serum glutamic-oxaloacetic transaminase (SGOT), serum glutamate pyruvate transaminase (SGPT) =\< 3 X ULN if no liver metastasis present (obtained less than 4 weeks from study entry)
* SGOT, SGPT =\< 5 X ULN if liver metastasis present (obtained less than 4 weeks from study entry)
* Human immunodeficiency virus (HIV): stable on antiretroviral therapy (ART) for at least 4 weeks, no documented evidence of multi-drug resistance, viral load of \< 400 copies/ml and CD4+ T-cells =\< 350 cells/uL (obtained less than 4 weeks from study entry)
* Hepatitis B virus (HBV)/hepatitis C virus (HCV): participant on a stable dose of antiviral therapy, HBV viral load below the limit of quantification. HCV viral load below the limit of quantification (obtained less than 4 weeks from study entry)
* Females of childbearing potential must not be breast feeding and must have a negative serum or urine pregnancy test within 7 days of starting of treatment. The patient must agree to use adequate contraception for a minimum of two weeks prior to receiving study medication until 65 days after discontinuation of the study medication. Acceptable methods of contraception include total and true sexual abstinence, hormonal contraceptives that are not prone to drug-drug interactions (IUS levonorgestrel intra uterine system \[Mirena\], medroxyprogesterone injections \[Depo-Provera\]), copper-banded intra-uterine devices, and vasectomized partner. All hormonal methods of contraception should be used in combination with the use of a condom by their sexual male partner. Females of childbearing potential are defined as those who are not surgically sterile (i.e., bilateral tubal ligation, bilateral oophorectomy, or complete hysterectomy) or postmenopausal (defined as 12 months with no menses without an alternative medical cause). Women will be considered post-menopausal if they have been amenorrheic for the past 12 months without an alternative medical cause. The following age-specific requirements must also apply: women \< 50 years old: they would be considered post-menopausal if they have been amenorrheic for the past 12 months or more following cessation of exogenous hormonal treatments. The levels of luteinizing hormone (LH) and follicle-stimulating hormone (FSH) must also be in the post-menopausal range (as per the institution). Women \>= 50 years old: they would be consider post-menopausal if they have been amenorrheic for the past 12 months or more following cessation of all exogenous hormonal treatments, or have had radiation-induced oophorectomy with the last menses \> 1 year ago, or have had chemotherapy-induced menopause with \> 1 year interval since last menses, or have had surgical sterilization by either bilateral oophorectomy or hysterectomy
* Non-sterilized males who are sexually active with a female partner of childbearing potential must use adequate contraception for the duration of the study and 125 days after the last dose of study medication. Adequate contraception methods include: birth control pills (e.g. combined oral contraceptive pill), barrier protection, and abstinence. Patients should not father a child for 125 days after completion of the study medication. Patients should refrain from donating sperm from the start of dosing until 125 days after discontinuing the study medication. If male patients wish to father children they should be advised to arrange for freezing of sperm samples prior to the start of the study medication

Exclusion Criteria:

* Previous treatments with cytotoxic chemotherapy or checkpoint immunotherapy or combination of chemo-immunotherapy for metastatic disease. If the patient had prior chemotherapy as neoadjuvant or adjuvant therapy, the completion of treatment must be greater than 6 months until the beginning of the treatment on trial
* Previous treatment with any anti-TGF-beta medications
* Spinal cord compression or brain metastases unless asymptomatic or stable for at least 2 weeks prior to start of study treatment
* Persisting grade \> 1 Common Terminology Criteria for Adverse Events (CTCAE) 5.0 toxicity (except alopecia and vitiligo) related to prior therapy; however, sensory neuropathy grade =\< 2 is acceptable
* Current use of immunosuppressive medication, EXCEPT for the following:

  * Intranasal, inhaled, topical steroids, or local steroid injection (e.g., intra-articular injection);
  * Systemic corticosteroids at physiologic doses =\< 10 mg/day of prednisone or equivalent;
  * Steroids as premedication for hypersensitivity reactions (e.g., computed tomography \[CT\] scan premedication).
* Active autoimmune disease that might deteriorate when receiving an immuno-stimulatory agent. Patients with diabetes type I, vitiligo, psoriasis, or hypo- or hyperthyroid diseases not requiring immunosuppressive treatment are eligible
* Any evidence of current interstitial lung disease (ILD) or pneumonitis or a prior history of ILD or non-infectious pneumonitis requiring high-dose glucocorticoids
* No previous malignant disease within the last 3 years except for a. superficial/non-invasive bladder cancer, or basal or squamous cell carcinoma in situ treated with curative intent; b. endoscopically resected gastrointestinal (GI) cancers limited to the mucosal layer without recurrence in \> 1 year
* No prior organ transplantation including allogenic stem-cell transplantation, except transplants that do not require immunosuppression
* Active infection requiring systemic therapy
* Live vaccination that has received or will receive within 30 days prior to the first administration of study intervention. Seasonal flu vaccines that do not contain a live virus are permitted. COVID-19 vaccines are permitted
* Known severe hypersensitivity (grade \>= 3 National Cancer Institute \[NCI\] CTCAE 5.0) to investigational product or any component in its formulations, any history of anaphylaxis, or recent, within 5 months, history of uncontrollable asthma
* Clinically significant (i.e., active) cardiovascular disease: cerebral vascular accident/stroke (\< 6 months prior to enrollment), myocardial infarction (\< 6 months prior to enrollment), unstable angina, congestive heart failure (\>= New York Heart Association Classification class II), or serious cardiac arrhythmia requiring medication
* History of bleeding diathesis or recent major bleeding events (i.e. grade \>= 2 bleeding events in the month prior treatment)
* Males and females of reproductive potential who are not using and effective method of birth control and females who are pregnant or breastfeeding or have a positive (urine or serum) pregnancy test prior to study entry. Females who are pregnant or breast-feeding
* Judgment by the investigator that the patient should not participate in the study if the patient is unlikely to comply with study procedures, restrictions and requirement