If you are keying the lattice points, you'll need to key them at a normal state first, and then key them again at a normal state a frame before you want the deformation to begin to occur.
For example. Let's say, I want the chess piece to move normally from frame 1-50, and deform. I want the deforming to take 15 frames. I'll key the lattice points at frame 1 in a normal state, and key them again at frame 50. Then, at frame 65, I'll deform and key the lattice points again.