"Owen (1859) initially described this taxon as the type species of a new genus, Ptychognathus, named for dicynodonts with anteroposteriorly short skulls with tall, strongly deflected snouts. In subsequent papers Owen variously treated Ptychognathus as a distinct genus (e.g. Owen, 1876) or a subgenus of Dicynodon (e.g., Owen, 1860). Although P. declivis was the first named species of Lystrosaurus, it was not combined in that genus until work by Brink (1951), who recognized the validity of the species over L. latirostris (Owen, 1860), which was previously in wide use for the exceptionally tall-snouted species of Lystrosaurus (Cluver 1971; Colbert, 1974; Grine et al., 2006) have all recognized the validity of L. declivis" from Kammerer et al., 2011.

Lystrosaurus declivis was named by Brink (1951). Its type specimen is NHMUK 36221, a skull, and it is a 3D body fossil. Its type locality is Rhenosterberg (Lystrosaurus Assemblage Zone), which is in an Induan terrestrial siliciclastic in the Katberg Formation of South Africa.