• Pre-Registration - Inclusion Criteria Specific to Dose Escalation Cohort

‣ Histolopathological and/or molecular confirmation of either glioblastoma, IDH wildtype (GBM), (as defined by either the 2016 or 2021 World Health Organization \[WHO\] classifications) anaplastic astrocytoma, IDH wildtype (AA) (as defined by the 2016 WHO classification) or non-small cell lung cancer (NSCLC)

⁃ EGFR Status:

• GBM/AA must either EGFR amplification and/or any activating EGFR mutation (e.g. A289T, EGFRvIII , etc.)

∙ NSCLC must have a confirmed activating EGFR mutation (e.g. Del19, L858R, EGFRvIII, G719A, L861Q, T790M, C797S, etc.)

• Pre-Registration - Inclusion Criteria Specific to Dose Expansion Cohorts

‣ Glioblastoma, IDH wildtype/Anaplastic astrocytoma, IDH wildtype (GBM/AA) Cohort:

• Diagnosis: Histological or molecular confirmation of either glioblastoma, IDH wildtype (GBM) (as defined by either the 2016 or 2021 WHO classifications) or anaplastic astrocytoma, IDH wildtype (AA) (as defined by the 2016 WHO classification)

∙ EGFR status: GBM/AA must have EGFRvIII mutation

⁃ Brain Tumor Penetration (BTP) Cohort:

• Diagnosis: Histopathological or molecular confirmation of either glioblastoma, IDH wildtype (GBM) (as defined by either the 2016 or 2021 WHO classifications) or anaplastic astrocytoma, IDH wildtype (AA) (as defined by the 2016 WHO classification)

∙ EGFR status: GBM/AA must have been previously demonstrated to have either EGFR amplification and/or any activating EGFR mutation based on any prior resection

⁃ Non-Small Cell Lung Cancer (NSCLC) cohort:

• Diagnosis: Histological confirmation of non-small cell lung cancer (NSCLC)

∙ EGFR status: NSCLC must have confirmed activating EGFR mutation. Following protocol amendment 7, NSCLC must have EGFR C797S mutation.

• Registration -Inclusion Criteria Specific to Dose Escalation Cohort

‣ Previous treatments:

• Patients with GBM/AA must have been previously treated with radiation and temozolomide

∙ Patients with NSCLC must have been previously treated with at least one line of single-agent therapy with an EGFR TKI e.g. gefitinib, erlotinib, afatinib, or osimertinib)

⁃ Radiographic progression:

• Patients with GBM/AA must have radiographic progression based on RANO criteria

∙ Patients with NSCLC must have new or radiographic progression in the central nervous system (brain metastases and/or leptomeningeal metastases). Positive confirmation of CSF cytology is both necessary and sufficient to define the presence of leptomeningeal metastases for patients in this study. Patients with positive CSF cytology and brain metastases will be categorized as leptomeningeal metastases.

⁃ Measurable disease

⁃ Eastern Cooperative Oncology Group (ECOG) 0 or 1. For patients with NSCLC with leptomeningeal metastases, ECOG 2 is also acceptable

• Registration - Inclusion Criteria Specific to Dose Expansion Cohorts

‣ Glioblastoma, IDH wildtype/Anaplastic astrocytoma, IDH wildtype (GBM/AA) Cohort:

• Previous treatments: Patients must have been previously treated with radiation and temozolomide. First recurrence only (no additional systemic therapies have been administered for recurrent disease)

∙ Radiographic progression: Patients with GBM/AA must have radiographic progression based on RANO criteria

∙ Patients remain eligible for enrollment if the recurrent disease has been surgically removed

∙ Performance status: ECOG 0 or 1

⁃ Brain Tumor Penetration (BTP) Cohort:

• Previous treatments: Patients must have been previously treated with radiation and temozolomide

∙ Radiographic progression: Patients with GBM/AA must have radiographic progression based on RANO criteria

∙ Therapeutic surgical resection of GBM/AA required as part of routine clinical care

∙ Performance status: ECOG 0 or 1

⁃ Non-Small Cell Lung Cancer (NSCLC) cohort:

• Previous treatments: No limitations

∙ Radiographic progression: Patients must have radiographic progression based on RECIST 1.1 criteria.

∙ Measurable Disease

∙ Performance Status: ECOG 0 or 1

• Registration - Inclusion Criteria Common to Dose Escalation and Dose Expansion Cohorts:

‣ Age \>= 18 years old

⁃ Ability to understand and the willingness to sign a written informed consent document

⁃ Hemoglobin \>= 9.0 g/dL (obtained =\< 14 days prior to registration)

⁃ Leukocytes \>= 3.0 x 10\^9/L (obtained =\< 14 days prior to registration)

⁃ Absolute neutrophil count \>= 1.5 x 10\^9/L (obtained =\< 14 days prior to registration)

⁃ Platelets \>= 100 x 10\^9/L (obtained =\< 14 days prior to registration)

⁃ International normalized ratio (INR) =\< 1.5 x upper limit of normal (ULN) (obtained =\< 14 days prior to registration)

• Patients on a stable dose of anti-coagulation therapy will be allowed to participate if they have no signs of bleeding or clotting and the INR/prothrombin time (PT) and partial thromboplastin time (PTT)/activated (a)PTT results are compatible with an acceptable risk-benefit ratio as per the investigator's discretion

⁃ aPTT =\< 1.5 x ULN (obtained =\< 14 days prior to registration)

• Patients on a stable dose of anti-coagulation therapy will be allowed to participate if they have no signs of bleeding or clotting and the INR/PT and PTT/aPTT results are compatible with an acceptable risk-benefit ratio as per the investigator's discretion

⁃ Total bilirubin =\< 1.5 x ULN and =\< 3 mg/dL for patients with Gilbert's disease (obtained =\< 14 days prior to registration)

⁃ Aspartate aminotransferase (AST) (serum glutamic-oxaloacetic transaminase \[SGOT\]) and alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) =\< 3 x ULN or =\< 5 x ULN if due to liver involvement by tumor (obtained =\< 14 days prior to registration)

⁃ Creatinine =\< 1.5 x ULN or estimated glomerular filtration rate (estimated glomerular filtration rate \[eGFR\]) \>= 60 mL/minute (obtained =\< 14 days prior to registration)

⁃ Negative pregnancy test done =\< 7 days prior to registration, for persons of childbearing potential only

⁃ Provision of signed and dated written informed consent prior to any study specific procedures, sampling, and analyses

⁃ Willingness to provide mandatory blood specimens for correlative research

⁃ Willingness to return to enrolling institution for follow-up (during the active monitoring phase of the study i.e., active treatment and clinical follow-up)

⁃ Male and female patients of child bearing potential must be willing to use contraception, (i.e., condoms, birth control) while on study and until 3 months after the last dose of study drug is taken

⁃ Must be willing to take light-protective measures during the study and for 2 weeks after their last dose of WSD0922-FU

⁃ Must have a minimum life expectancy of \>= 3 months

⁃ Must be stable on no more than 2 mg of dexamethasone (or equivalent steroids) per day. Steroid dose adjustments should be minimized during cycle 1 of therapy. Patients enrolling to the BTP expansion cohort do not have any restrictions on current steroid/dexamethasone dosing.

⁃ Must not take enzyme-inducing anticonvulsants treatment for at least 2 weeks prior to enrollment. Patients on enzyme-inducing anticonvulsants will be changed to non-enzyme inducing anticonvulsants

⁃ Strong inducers and strong inhibitors of CYP3A should be discontinued at least 14 days prior to registration

⁃ Willingness to provide mandatory tissue specimens for correlative research (BTP cohort only)