Fungal laccases catalyze a wide range of reactions that have fostered an escalating demand in diverse sectors. Higher productivity in a short period remains a major challenge that needs to be fulfilled for successful industrial applications. In the present study, statistical optimization methods were utilized for high-yielding laccase production by the fungus Trametes maxima IIPLC-32 that achieved 103 IU mL⁻¹ activity and a 13.3-fold increase compared to that under unoptimized conditions. Optimization using the Plackett–Burman design (PBD) and Box–Behnken design (BBD) identified that glucose, xylidine, veratryl alcohol, CuSO₄, and potassium phosphate significantly influenced the laccase production. Furthermore, it also revealed that glucose contributed maximally to the overall laccase production, followed by xylidine and veratryl alcohol. Mathematical models were used for kinetic analysis. Kinetics of biomass formation followed the logistic growth model (with the model parameter values of X_max = 9.54 g L⁻¹, μ_max = 0.77 d⁻¹, and R² = 0.95). Laccase production kinetics followed the Luedeking–Piret model (with the model parameters of α = 0.12 IU mg⁻¹, β = 1.57 IU mg⁻¹ d⁻¹, and R² = 0.90), indicating that the laccase produced by Trametes maxima IIPLC-32 is partially growth associated. The logistic mass balance equation adequately described substrate utilization. The model parameters of Y_x/s = 0.96 g g⁻¹ and m = 0.05 g g⁻¹ d⁻¹ were retrieved from the logistic mass balance equation. The applicability of the enzyme produced from the optimized process was checked for the decolorization of remazol brilliant blue R, and the maximum decolorization efficiency of 92.3% was achieved within 8 h of reaction without the addition of a mediator.