Due to their low cost and ability to synthesize lipids for sustainable biodiesel production, oleaginous fungus has recently gained more prominence than other microorganisms. The new oleaginous fungus Aspergillus carneus OQ275240’s dry biomass, lipid content, and lipid yield were all optimized in this work, using the response surface methodology-based Box–Behnken design. Analysis of variance (ANOVA) was also used to examine the experimental data, and multiple regression analysis was used to fit the data to a second-order polynomial equation. Three independent variables, such as the concentration of yeast, glucose, and phosphorus, were examined for their mutual impacts. Maximum dry biomass (0.024 g/50 mL), lipid content (36.20%), and lipid yield (8.70 mg/50 mL) were achieved at optimal concentrations of 2.68 g/L of yeast, 20.82 g/L of glucose, and 0.10 g/L of phosphorus, respectively, showing that the actual data and predictions of the models were in good agreement. A. carneus OQ275240 has a favorable fatty acid profile that can be used to successfully create biodiesel, as shown by the presence of palmitic acid (C16:0), stearic acid (C18:0), and oleic acid (C18:1) in its fatty acid methyl esters (FAMEs) profile. Furthermore, the qualities of the biodiesel were investigated, and it was found that they fell within the parameters established by the international specifications EN 14214 (Europe) and ASTM D6751-08 (United States). These findings point to the newly evaluated filamentous fungal strain as a potential feedstock for the production of high-quality biodiesel.