It is shown, based on the density functional theory (DFT), that the spin splitting of surface electronic states induced by a Pb monolayer on the Ge(111)-1 x 1 surface depends on the bonding structure of the Pb/Ge interface and may be either significant, similar to 0.8 eV, (H-3/T-4) or completely suppressed (T-1). It is also shown that for the former the bonding configuration facilitates an emergence of unquenched orbital angular momentum L along Gamma-K-M direction, which then lifts the spin degeneracy of the electronic states through the spin-orbit coupling (SOC) of electrons in Pb. Along with the DFT data, we present a complementary analysis conducted withing the orbital Rashba framework, which provides an additional insight into the SOC-induced splitting.