In cruise flight of an aircraft lift does no work, it just holds the aircraft aloft. In order to climb aircraft pitch up and need excess energy because the thrust vector now has a vertical component acting against gravitational acceleration.
Please take a look at the following cart. The thrust gets delivered by a propeller at the rear and the thrust vector is always horizontal. A wing is attached to a vertical pole.
An experiment is done with the following steps:
The cart is at rest and the wing is locked to the pole. Then the cart is accelerated and when it reaches terminal velocity the engine is turned off and the locking of the wing is released at the same time.
When the lift produced by the wing is greater than its weight, the wing begins to accelerate vertically. At some point the wing reaches a vertical terminal velocity at which further acceleration stops. The drag onto the cart is greater when the wing moves upwards compared to when it does not.
The drag slows down the cart. The kinetic energy of the cart is converted into thermal energy (some of the cart’s kinetic energy is transferred onto the surrounding air, but in the end all dissipates to thermal energy).
Conclusion: The kinetic energy of the cart is converted entirely into thermal energy. No kinetic energy of the cart goes into potential energy of the wing, the movement of the wing is done purely by lift.
Did I miss something?