Non-small cell lung cancer (NSCLC) is the most prevalent subtype of lung cancer and a leading cause of cancer-related mortality worldwide. Literature evidences indicates a strong association between systemic inflammation, driven by cytokines such as Interleukin-6 (IL-6), and the development of NSCLC-associated sarcopenia. However, the immuno-metabolic underpinnings that link tumor-derived IL-6 signaling to skeletal muscle degradation remain incompletely understood. We developed a comprehensive immuno-metabolic mathematical model to investigate how IL-6 signaling influences branched-chain amino acids (BCAA) metabolism and redox homeostasis in the context of NSCLC-induced sarcopenia by understanding two key causes of sarcopenia which are malnutrition and redox homeostasis. Our model integrates IL-6-mediated activation of the Janus Kinase (JAK)/Signal transducer and activator of transcription 3 (STAT3) pathway, highlighting the differential roles of STAT3 phosphorylation at S727 (mitochondrial electron transport chain (ETC) activation) and Y705 (nuclear translocation and transcriptional regulation of oncogenes Hypoxia-Inducible Factor 1, alpha (HIF-1) and cellular Myc (c-Myc). These transcription factors reprogram tumor metabolism by upregulating glucose and amino acid transporters, including those specific to BCAAs. In skeletal muscle, elevated IL-6 disrupts insulin signaling via Suppressor of cytokine signaling 3 (SOCS3), suppresses Mechanistic Target of Rapamycin Complex 1 (mTORC1) activation, and enhances oxidative stress, collectively contributing to impaired protein synthesis, increased proteolysis, and muscle wasting. BCAA dysregulation further impairs metabolic balance and exacerbates sarcopenia through defective Tricarboxylic Acid Cycle (TCA) input and epigenetic modulation via acetyl coenzyme A (acetyl-CoA) and S-Adenosylmethionine (SAM). Our model reveals a central role for IL-6-driven metabolic rewiring, particularly BCAA utilization and redox imbalance, in promoting NSCLC-induced sarcopenia. These findings underscore the dual impact of IL-6 on tumor progression and systemic muscle degradation, and provide a framework for evaluating therapeutic strategies that target IL-6/STAT3 signaling and amino acid metabolism via STAT3 and acetyl-CoA cross talk to mitigate NSCLC-induced sarcopenia.