Converts glycerol-3-phosphate to 1-acyl-sn-glycerol-3-phosphate (lysophosphatidic acid or LPA) by incorporating an acyl moiety at the sn-1 position of the glycerol backbone (PubMed:18238778). Active against both saturated and unsaturated long-chain fatty acyl-CoAs (PubMed:18238778). Protects cells against lipotoxicity (PubMed:30846318).