Nernst Equation for Lithium ion battery
The Nernst equation for the anode is :$$E_a = E°_a + \frac{RT}{F}ln{\frac{[Li^+]_e [C_6]_s}{[LiC_6]_s}}$$ where the concentrations $[C_6]_s$ and $[LiC_6]_s$ are  defined in the solid phase of the anode, and not in the electrolyte. The concentration $[Li^+]_e$ is defined in the electrolyte. When the anode is working, the concentration $[LiC_6]_s$ decreases in the solid phase and the concentration $[C_6]_s$ increases.

The same reasoning may be done on the Nernst equation at the cathode :  $$E_c = E°_c + \frac{RT}{F}· ln{\frac{[Li^+]_e[CoO_2]_{s'}}{[LiCoO_2]_{s'}}}$$ where $[CoO_2]_{s'}$ is the concentration of $CoO_2$ in the solid phase of the cathode, and $[LiCoO_2]_{s'}$ is the concentration of $LiCoO_2$ in the solid phase of the cathode. 

The overall voltage of the battery $\Delta E$ can be written :  $$\Delta E = E°_c - E°_a + \frac{RT}{F} · ln\frac{[LiC_6]_s [CoO_2]_{s'}}{[C_6]_s [LiCoO_2]_{s'}}$$ As a consequence, both $[LiC_6]_s$ and $ [CoO_2]_{s'}$ decrease when the battery is working. So the overall voltage decreases.