Catalyzes the aldol-type condensation of 2-oxoglutarate with acetyl-CoA to yield homocitrate. Carries out the first step of the alpha-aminoadipate (AAA) lysine biosynthesis pathway. 2-oxoglutarate + acetyl-CoA + H2O = (2R)-homocitrate + CoA + H(+) Inhibited by lysine. kcat is 1.4 sec(-1). Amino-acid biosynthesis; L-lysine biosynthesis via AAA pathway; L-alpha-aminoadipate from 2-oxoglutarate: step 1/5. Forms a homotetramer in the absence of lysine, and is in hexadecamer-octamer equilibrium in the presence of lysine. Contains an N-terminal catalytic domain fused with a RAM (Regulation of Amino acid Metabolism) domain at the C-terminus. The mutant enzyme lacking the RAM domain is insensitive to inhibition by lysine, indicating that the RAM domain is responsible for enzyme allosteric regulation. Moreover, the mutant enzyme lacking the RAM domain forms homodimer irrespective of the presence of lysine, which suggests that HCS undergoes changes in its oligomeric state by binding lysine at its RAM domain. Belongs to the alpha-IPM synthase/homocitrate synthase family. Homocitrate synthase LYS20/LYS21 subfamily.