Hydrolyzes specifically phosphatidic acid (PA) to produce 2-acyl lysophosphatidic acid (LPA; a potent bioactive lipid mediator) and fatty acid (By similarity). Does not hydrolyze other phospholipids, like phosphatidylserine (PS), phosphatidylcholine (PC) and phosphatidylethanolamine (PE) or triacylglycerol (TG) (By similarity). 1-hexadecanoyl-2-(9Z-octadecenoyl)-sn-glycero-3-phosphate + H2O = 2-(9Z-octadecenoyl)-sn-glycero-3-phosphate + H(+) + hexadecanoate Expressed in liver and lacrimal gland. Belongs to the AB hydrolase superfamily. Lipase family.