In this study, we examine the influence of the soundboard thickness profile and bracing pattern on the vibrational and acoustic behavior of the Lute using finite element simulations. A fully parametric model of the instrument body was developed and combined with a full factorial design (2 × 32) to systematically explore the effects of these parameters. Numerical modeling is employed to evaluate the acoustic performance of the Lute in terms of sound pressure level and sound balance. Although several studies have investigated the acoustics of string instruments such as guitars and violins, the Lute remains insufficiently studied from a structural–acoustic interaction perspective. According to the literature, no previous work has integrated a full factorial design with harmonic acoustic simulations and multi-objective optimization to simultaneously evaluate sound pressure level and sound balance. This methodological framework and its findings represent the principal contribution of the present work.