A rechargeable battery that employs a Li metal anode requires that Li be plated in a uniform fashion during charging. In "anode-free" configurations, this plating will occur on the surface of the Cu current collector (CC) during the initial cycle and in any subsequent cycle where the capacity of the cell is fully accessed. Experimental measurements have shown that the plating of Li on Cu can be inhomogeneous, which can lower the efficiency of plating and foster the formation of Li dendrites. The present study employs a combination of first-principles calculations and sessile drop experiments to characterize the thermodynamics and adhesive (i.e., wetting) properties of interfaces involving Li and other phases present on or near the CC. Interfaces between Li and Cu, Cu2O, and Li2O are considered. The calculations predict that both Cu and Cu2O surfaces are lithiophilic. However, sessile drop measurements reveal that Li wetting occurs readily only on pristine Cu. This apparent discrepancy is explained by the occurrence of a spontaneous conversion reaction, 2 Li + Cu2O → Li2O + 2 Cu, that generates Li2O as one of its products. Calculations and sessile drop measurements show that Li does not wet (newly formed) Li2O. Hence, Li that is deposited on a Cu CC where surface oxide species are present will encounter a compositionally heterogeneous substrate comprising lithiophillic (Cu) and lithiophobic (Li2O) regions. These initial heterogeneities have the potential to influence the longer-term behavior of the anode under cycling. In sum, the present study provides insights into the early stage processes associated with Li plating in anode-free batteries and describes mechanisms that contribute to inefficiencies in their operation.