The 3rd class of BRAF (B-Raf Proto-Oncogene, Serine/Threonine Kinase) variants including G466, D594, and A581 mutations cause kinase death or impaired kinase activity. It is unlikely that RAF (Raf Proto-Oncogene, Serine/Threonine Kinase) inhibitors suppress ERK (Extracellular Signal-Regulated Kinase) signaling in class 3 mutant-driven tumors due to the fact that they preferentially inhibit activated BRAF V600 mutants. However, there are suggestions that class 3 mutations are still associated with enhanced RAS/MAPK (RAS Proto-Oncogene, GTPase/Mitogen-Activated Protein Kinase) activation, potentially due to other mechanisms such as the activation of growth factor signaling or concurrent MAPK pathway mutations, e.g., RAS or NF1 (Neurofibromin 1). A 75-year-old male patient with squamous-cell cancer (SqCC) of the lung and with metastases to the kidney and mediastinal lymph nodes received chemoimmunotherapy (expression of Programmed Cell Death 1 Ligand 1 (PD-L1) on 2% of tumor cells). The chemotherapy was limited due to the accompanying myelodysplastic syndrome (MDS), and pembrolizumab monotherapy was continued for up to seven cycles. At the time of progression, next-generation sequencing was performed and a c.1781A>G (p.Asp594Gly) mutation in the BRAF gene, a c.1381C>T (p.Arg461Ter) mutation in the NF1 gene, and a c.37C>T (p.Gln13Ter) mutation in the FANCC gene were identified. Combined therapy with BRAF (dabrafenib) and MEK (trametinib) inhibitors was used, which resulted in the achievement of partial remission of the primary lesion and lung nodules and the stabilization of metastatic lesions in the kidney and bones. The therapy was discontinued after five months due to myelosuppression associated with MDS. The molecular background was decisive for the patient’s fate. NSCLC patients with non-V600 mutations in the BRAF gene rarely respond to anti-BRAF and anti-MEK therapy. The achieved effectiveness of the treatment could be related to a mutation in the NF1 tumor suppressor gene. The loss of NF1 function causes the excessive activation of KRAS and overactivity of the signaling pathway containing BRAF and MEK, which were the targets of the therapy. Moreover, the mutation in the FANCC gene was probably related to MDS development. The NGS technique was crucial for the qualification to treatment and the prediction of the NSCLC course in our patient. The mutations in two genes—the BRAF oncogene and the NF1 tumor suppressor gene—were the reason for the use of dabrafenib and trametinib treatment. The patients achieved short-term disease stabilization. This proved that coexisting mutations in these genes affect the disease course and treatment efficacy.