Transition metal phthalocyanine molecules adsorbed on a metal substrate exhibit rich spin-related phenomena such as magnetic anisotropy, spin excitation, and Kondo effect. In this work, we investigate theoretically few-layer cobalt phthalocyanine (CoPc) molecular assembly stacking on Pb(111) surface with the use of a combined density functional theory (DFT) and hierarchical equations of motion (HEOM) approach. Calculation results indicate that the local spin properties of CoPc/Pb(111) composites depend critically on the number of adsorption layers. The first layer of CoPc on the Pb(111) surface serves as a spin-insulating buffer, while the CoPc molecules in the second layer exhibit spin-1/2 Kondo effect with a Kondo temperature of about 22 K. In a triple-layer CoPc assembly stacking on Pb(111), the antiferromagnetic coupling between the second and third layers leads to local spin-flip excitations under finite bias voltages, which gives rise to characteristic signatures in the differential conductance spectra. The DFT+HEOM approach thus provides a practical means for investigating the local electronic and spin properties of two-dimensional molecular assemblies adsorbed on the metal surface. The insights obtained from the first-principles based simulations could be useful for experimental manipulation or design of magnetic composite systems.