Transition from one terrain to another over time?

I have two overlapping terrains that are very similar (same width/height and position) but they have different height maps.

I was wondering if it is possible to transition (or morph) from one terrain to the other over time?

The first terrain is very flat and the second terrain has hills. What I was hoping to find was a way I can make it appear as if the first terrain slowly turns into the second terrain (appearing like hills are growing out of the flat terrain over time).

Any suggestions? And would baked lightmaps be a problem with any approach?