Catalyzes the NAD(+)-dependent conversion of homoisocitrate to alpha-ketoadipate. (2R,3S)-homoisocitrate + NAD(+) = 2-oxoadipate + CO2 + NADH Binds 1 Mg(2+) ion per subunit. Inhibited by the reaction product NADH. Inhibited by oxalate; this is a non-competitive inhibitor. The KM for homoisocitrate is lower than 10 uM. Optimum pH is 8.3-8.8 for the forward reaction, and 7 for the reverse reaction. Amino-acid biosynthesis; L-lysine biosynthesis via AAA pathway; L-alpha-aminoadipate from 2-oxoglutarate: step 4/5. Activity is repressed 4-fold by lysine. Present with 19079 molecules/cell in log phase SD medium. Belongs to the isocitrate and isopropylmalate dehydrogenases family.