A plane requires less lift to climb than for level flight. Doesn't make much sense, does it? Lets start by looking at the forces on a plane in level flight and then we will go from there. in level flight all of the forces are in equilibrium. The airplane is maintaining a constant airspeed and altitude. Thrust equals Drag and Lift equals Weight.
T = D
L = W
Now if we were to increase the thrust one of two things would have to happen. First the plane could accelerate in level flight until a new equilibrium has been reached or you could maintain the same airspeed by raising the nose and climbing the plane. It is fairly simple to state that more thrust is required to climb, but why less lift? After all, the plane is not getting any lighter. To answer that question lets draw a vector diagram of the forces acting on a plane in the climb.
T = D + W sin a
L = W cos a
Essentially what is happening is that Weight is no longer directly opposed to Lift. The Weight vector is now divided into two with a portion (sin a) acting along the same line as Drag, hence, the need for more thrust. Secondly, a portion of the Weight vector (cos a) is still acting against Lift and therefore, less Lift is required. As the angle of climb increases then more Weight acts along with Drag and less opposes Lift. Looking at it from an extreme point of view. Let's say that a plane was going vertically upwards and the angle of climb is 900. Now the Thrust must equal Drag plus all of the Weight (sin 90 = 1) and there is no Weight for Lift to oppose (cos 90 = 0) and therefore, no Lift is required in a vertical climb.