The asymmetric biraphid pennate diatom Amphora copulata, isolated from tropical coastal waters (South China Sea, Malaysia), was cultured for renewable production of lipids (oils) in a medium comprised of inorganic nutrients dissolved in dilute palm oil mill effluent (POME). Optimal levels of nitrate, phosphate, and silicate were identified for maximizing the biomass concentration in batch cultures conducted at 25 ± 2 °C under an irradiance of 130 µmol m−2 s−1 with a 16 h/8 h light-dark cycle. The maximum lipid content in the biomass harvested after 15-days was 39.5 ± 4.5% by dry weight in a POME-based medium with optimal levels of nitrate, phosphate, and silicate. Under the optimized conditions the maximum dry mass concentration of the diatom was 660 mg L−1 on day 12, declining to ~650 mg L−1 on day 15. For the 15-day batch operation, the final average productivities of the biomass and the lipids were 43.3 ± 4.5 mg L−1 d−1 and 17.1 ± 0.3 mg L−1 d−1, respectively. The fatty acids in the diatom lipids were found to be (%, w/w of total lipids): palmitoleic acid (39.8%), palmitic acid (31.9%), myristic acid (6.8%), oleic acid (4.7%), stearic acid (4.5%), arachidonic acid (3.9%), eicosapentaenoic acid (3.6%), linoleic acid (2.5%), tetracosanoic acid (1.7%), and linolenic acid (0.6%).