The conversion of methane into liquid biofuels using methane-consuming bacteria, known as methanotrophs, contributes to sustainable development, as it mitigates the problem of climate change caused by greenhouse gases and aids in producing cleaner and renewable energy. In the present research, an efficient methanotroph, Methylosarcina sp. LC-4, was studied as a prospective organism for biodiesel production using methane. The methane uptake rate by the organism was enhanced 1.6 times and 2.35 times by supplementing LC-4 with micronutrients, such as copper and tungstate, respectively. This unique ability of the isolated organism enables the deployment of methanotrophs-based processes in various industrial applications. A Plackett–Burman statistical (PBD) design was used to quantify the role of the micronutrients and other media components present in the nitrate minimal salt media (NMS) in biomass and fatty acid methyl esters (FAME) yields. Nitrate, phosphate, and tungstate had a positive effect, whereas copper, magnesium, and salinity had a negative effect. The modified NMS media, formulated according to the results from the PBD analysis, increased the FAME yield (mg/L) by 85.7%, with the FAME content of 13 ± 1% (w/w) among the highest reported in methanotrophs. The obtained FAME consisted majorly (~90%) of C14–C18 saturated and monounsaturated fatty acids, making it suitable for use as biodiesel.