Catalyzes the transfer of the lipoyl group from lipoyl-AMP to the specific lysine residue of lipoyl domains of lipoate-dependent enzymes. (R)-lipoyl-5'-AMP + L-lysyl-[lipoyl-carrier protein] = (R)-N(6)-lipoyl-L-lysyl-[lipoyl-carrier protein] + AMP + 2 H(+) Protein modification; protein lipoylation via exogenous pathway; protein N(6)-(lipoyl)lysine from lipoate: step 2/2. Belongs to the LplA family.