Catalysis of the reaction: UDP-N-acetylmuramoyl-L-alanyl-D-glutamate + D-lysinium(1+) + ATP = UDP-N-acetylmuramoyl-L-alanyl-gamma-D-glutamyl-D-lysine + ADP + hydrogenphosphate + H+.
UDP-N-acetylmuramoyl-L-alanyl-D-glutamate--D-lysine ligase activity