Weight loss interventions in individuals with overweight or obesity result in reductions in both fat mass and lean body mass (LBM). While fat loss is the primary therapeutic target, preserving LBM may have favorable health implications. This narrative review evaluates the role of amino acid supplementation, including essential amino acids (EAAs) and branched-chain amino acids (BCAAs), in supporting the preservation of LBM during weight loss induced by lifestyle interventions, pharmacotherapy, or bariatric surgery. This is a narrative review of preclinical and clinical studies examining the effects of amino acid supplementation during calorie restriction on body composition and, when available, functional outcomes. A comprehensive search was conducted in the PubMed, Scopus, and Web of Science databases. Evidence suggests that EAA and peptide-based supplementation may help preserve LBM during periods of reduced energy intake, particularly when protein intake from whole foods is limited. Benefits appear more consistent when supplementation is combined with resistance exercise. BCAA supplementation alone has shown variable effects, especially in sedentary individuals or when total protein intake is already sufficient. Anabolic resistance associated with obesity may attenuate the muscle protein synthesis response to dietary amino acids. Amino acid supplementation may support the maintenance of LBM during weight loss, particularly under conditions of low protein intake or in conjunction with exercise. Further research is needed to determine the clinical significance of LBM changes and identify optimal supplementation strategies.