A gas lift valve system for a wellbore within a subterranean formation can include a power source that generates power, and a delivery system disposed within the wellbore and electrically coupled to the power source, where the delivery system delivers the power generated by the power source. The system can also include at least one gas lift valve assembly disposed within the wellbore and electrically coupled to the delivery system, where the at least one gas lift valve assembly receives the power from the delivery system, where at least one valve, when in a position other than a fully closed position, allows a control medium to flow from an inlet channel to an outlet channel, where the outlet channel empties into the cavity of the delivery system.