Catalyzes the NAD(+)-dependent oxidative decarboxylation of homoisocitrate to 2-oxoadipate (alpha-ketoadipate), a reaction involved in lysine biosynthesis through the alpha-aminoadipate pathway (PubMed:21813504). In addition, has high activity with isocitrate, but is inactive with 3-isopropylmalate (By similarity). (2R,3S)-homoisocitrate + NAD(+) = 2-oxoadipate + CO2 + NADH D-threo-isocitrate + NAD(+) = 2-oxoglutarate + CO2 + NADH Binds 1 Mg(2+) ion per subunit. Competitively inhibited by (2S,3S)-thiahomoisocitrate in vitro. Amino-acid biosynthesis; L-lysine biosynthesis via AAA pathway; L-alpha-aminoadipate from 2-oxoglutarate: step 4/5. Homotetramer. Dimer of dimers. The homotetramer can transiently dissociate into homodimers. Belongs to the isocitrate and isopropylmalate dehydrogenases family.