We present CCSD(T) interaction energies and the bonding analysis for complexes of Cu, Ag, and Au with the lone-pair ligands H2O, OF2, OMe2, NH3, NF3, NMe3, H2S, SF2, SMe2, PH3, PF3, PCl3, and PMe3 (ML complexes). Both electron correlation and relativistic effects are crucial in the bonding of all complexes. AuPH3, AuPF3, and AuPCl3 (AuPX3) complexes exhibit particularly large relativistic effects, 30-46 kJ/mol. Upon neglecting relativistic effects, the Au-P bonds almost vanish aside from weak long-range van der Waals interactions. Highest binding energies are computed for complexes with Au, followed by Cu and Ag. For all coinage metals the strongest interactions are computed for PX3 ligands followed by SX2 and NX3 OX2 ligands. Upon methylation the interaction energy rises significantly. Metal-thiol complexes, particularly AuSCH3, form a separate class. Exceptional stability of gold complexes is due to large relativistic enhancement of the electron affinity of Au. Along with the electron affinity of a metal, we link the pattern of interaction energies in ML complexes with ionization potentials (IPs) of ligands. Strong interaction with P containing ligands is attributed to their lower IP and the lone pair -> metal electron donation accompanied with the back-donation characteristic for P containing ligand. Energy data are accompanied with the natural bond orbital analysis. Computationally less demanding DFT computations with the PBE0 functional provide correct pattern of interaction energies when compared with benchmark CCSD(T) results.