In this study, biocatalysts in the form of mycelium-bound lipases of psychrotrophic and mesophilic fungi were screened for their ability to synthesize fatty acid methyl (FAME) and ethyl esters (FAEE). It has been shown that the hydrolytic activity of biocatalysts is not accompanied by their biodiesel synthetic activity. Preliminary studies showed for the first time, that the FTIR technique can be used to predict synthetic activity. The highest correlation between the intensity of the bands and synthetic activity, negative and positive, respectively, was observed for two neighboring bands at 1745 cm−1 (R = −0.73) and 1699 cm−1 (R = 0.68). The psychrotrophic strain Penicillium sp. 59, isolated from the soil of the Arctic tundra (Spitsbergen), has been shown for the first time as an efficient whole-cell biocatalyst for fatty acid ethyl ester synthesis and is stable in organic solvents. Mathematical optimization of biosynthesis was also performed using RSM. A molar canola oil conversion value of 83.3% into FAEE was obtained at 24.2 °C in n-hexane using 7.6% of used canola oil and 5.3% of the fungal biocatalyst within 6 h. Dry mycelium of Penicillium sp. 59 is a promising new biocatalyst for large-scale biosynthesis of biodiesel, given its low-cost production, high activity at room temperature, no need to mix reactions, and reusability in a minimum of six cycles.