Catalyzes the condensation of (S)-aspartate-beta-semialdehyde [(S)-ASA] and pyruvate to 4-hydroxy-tetrahydrodipicolinate (HTPA). L-aspartate 4-semialdehyde + pyruvate = (2S,4S)-4-hydroxy-2,3,4,5-tetrahydrodipicolinate + H(+) + H2O Is not feedback inhibited by lysine. Amino-acid biosynthesis; L-lysine biosynthesis via DAP pathway; (S)-tetrahydrodipicolinate from L-aspartate: step 3/4. Homodimer. Belongs to the DapA family. Was originally thought to be a dihydrodipicolinate synthase (DHDPS), catalyzing the condensation of (S)-aspartate-beta-semialdehyde [(S)-ASA] and pyruvate to dihydrodipicolinate (DHDP). However, it was shown in E.coli that the product of the enzymatic reaction is not dihydrodipicolinate but in fact (4S)-4-hydroxy-2,3,4,5-tetrahydro-(2S)-dipicolinic acid (HTPA), and that the consecutive dehydration reaction leading to DHDP is not spontaneous but catalyzed by DapB.