Catalyzes the migration of the L-beta-lysine and D-lysine epsilon amino group to the delta carbon to produce 3,5-diaminohexanoate and 2,5-diaminohexanoate, respectively. (3S)-3,6-diaminohexanoate = (3S,5S)-3,5-diaminohexanoate D-lysine = (2R,5S)-2,5-diaminohexanoate Amino-acid degradation; L-lysine degradation via acetate pathway. Heterotetramer of 2 alpha and 2 beta subunits. Belongs to the KamE family.