When a lithium-ion battery is being CHARGED (i.e. not in use or "discharged"), the flow of electrons and Li+ ions is
When the battery is charging, the lithium ions flow from the cathode to the anode, and the electrons move from the anode to the cathode. As long as lithium ions are making the trek from one electrode to another, there is a constant flow of electrons. This provides the energy to keep your device running.