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. Does not display 2-isopropylmalate synthase and citramalate synthase activities since it cannot use 2-oxoisovalerate or pyruvate as substrate. 2-oxoglutarate + acetyl-CoA + H2O = (2R)-homocitrate + CoA + H(+) Inhibited by lysine. Amino-acid biosynthesis; L-lysine biosynthesis via AAA pathway; L-alpha-aminoadipate from 2-oxoglutarate: step 1/5. 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. Cells lacking this gene do not grow in MM without or even with lysine, but grow in MM with the simultaneous supplementation of lysine and arginine to the medium. Furthermore, the mutant strain does not grow on MM supplemented with lysine and glutamate, but grows with lysine and ornithine. Belongs to the alpha-IPM synthase/homocitrate synthase family. Homocitrate synthase LYS20/LYS21 subfamily.