(2R,3S)-homoisocitrate + NAD(+) = 2-oxoadipate + CO2 + NADH Binds 1 Mg(2+) ion per subunit. Amino-acid biosynthesis; L-lysine biosynthesis via AAA pathway; L-alpha-aminoadipate from 2-oxoglutarate: step 4/5. Belongs to the isocitrate and isopropylmalate dehydrogenases family.