Catalyzes the aldol-type condensation of 2-oxoglutarate with acetyl-CoA to yield homocitrate (PubMed:19996101, PubMed:12095615). Carries out the first step of the alpha-aminoadipate (AAA) lysine biosynthesis pathway (PubMed:9868782). To a lesser extent, can also use oxaloacetate in place of 2-oxoglutarate, leading to citrate. Does not display 2-isopropylmalate synthase activity since it cannot use 2-oxoisovalerate (PubMed:12095615). 2-oxoglutarate + acetyl-CoA + H2O = (2R)-homocitrate + CoA + H(+) acetyl-CoA + H2O + oxaloacetate = citrate + CoA + H(+) Is highly and competitively inhibited by lysine that binds to the active site and competes with 2-oxoglutarate (PubMed:12095615, PubMed:19996101). Is also slightly inhibited by arginine and 2-aminoethylcysteine (PubMed:12095615). kcat is 92 min(-1) using 2-oxoglutarate as substrate (PubMed:12095615). kcat is 58 min(-1) using oxaloacetate as substrate (in the presence of KCl, necessary for activity) (PubMed:12095615). kcat is 41 min(-1) using 2-oxoglutarate as substrate (PubMed:19996101). Optimum temperature is 60 degrees Celsius. Activity is rapidly lost above 70 degrees Celsius. Amino-acid biosynthesis; L-lysine biosynthesis via AAA pathway; L-alpha-aminoadipate from 2-oxoglutarate: step 1/5. Exists in an equilibrium between monomer and homodimer. Cells lacking this gene show lysine auxotrophy, which can be complemented with alpha-aminoadipate but not with diaminopimelate. Belongs to the alpha-IPM synthase/homocitrate synthase family. Homocitrate synthase LYS20/LYS21 subfamily.