Catalyzes the transfer of the amino group of L-glutamate to [LysW]-aminoadipate 6-semialdehyde, generating [LysW]-gamma-L-lysine (Probable). In vitro, can use N(2)-acetyl-L-ornithine and N(2)-acetyl-L-lysine (PubMed:11489859). 2-oxoglutarate + [amino-group carrier protein]-C-terminal-gamma-(L-lysyl)-L-glutamate = [amino-group carrier protein]-C-terminal-N-(1-carboxy-5-oxopentan-1-yl)-L-glutamine + L-glutamate Binds 1 pyridoxal phosphate per subunit. kcat is 1.0 sec(-1) with N(2)-acetyl-L-ornithine as substrate. kcat is 0.8 sec(-1) with N(2)-acetyl-L-lysine as substrate. Amino-acid biosynthesis; L-lysine biosynthesis via AAA pathway; L-lysine from L-alpha-aminoadipate (Thermus route): step 4/5. Homodimer. Auxotroph for lysine. Belongs to the class-III pyridoxal-phosphate-dependent aminotransferase family. LysJ subfamily. Was originally thought (PubMed:11489859) to be an N(2)-acetyl-L-2-aminoadipate semialdehyde transaminase.