I think they start with Li on one side, and a Cu/C/S cathode on the other, and then plate the lithium on the anode. They measure a difference in chemical potentials between cathode and anode, so there is reason for the Li to move, and as the Li moves, I think I remember the V_cell decreasing.
From the paper:
> At the cathode, the build-up of plated metallic lithium changes the morphology of the cathode to increase C_C and create a very slow fade of V_cell with time of discharge