The problem is that finite wings inherently induce drag (called lift induced drag). Even if you could assume the wing infinite you still have parasitic drag. So you will always need to supply energy to keep the plane flying at a constant speed (and as a consequence to keep generating lift). Without drag it could, in principle, keep flying without power. It's the same with cars for example.
By the way the force that you are using in that equation should be the forward force (thrust) that compensates the drag, not the lift force, since lift is perpendicular to the velocity.
You could read this if you want a simple approximation to drag under certain conditions.