The LT only draws 150mA, so you can safely phantom power it from the Axe-Fx. You'll just need to find an AC adapter that will fit in the Axe-Fx's input - the one that comes with the LT does not. Any 9V AC or DC supply will be fine as long as the connector fits. Typically, 9VAC adapters have the connector that fits the Axe-Fx.