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(+) Amino-acid biosynthesis; L-lysine biosynthesis via AAA pathway; L-alpha-aminoadipate from 2-oxoglutarate: step 1/5. Belongs to the alpha-IPM synthase/homocitrate synthase family. Homocitrate synthase LYS20/LYS21 subfamily.