If I'm understanding right, the next wave comes up when the current wave is damaged around 35-50%. How come a lot of runners sacrifice lawnmowers early in a level then? Wouldn't you want to damage the first few zombies faster in order to get to the next waves? Is it so you can build up sunflowers/defend other lanes more comfortably?

I just want to try and understand better before I try running this c:

The reason we use lawnmowers at the start is so that we don't need to spend sun early on defences, and so we can set extra sunflowers up. Stalling for a mower also helps as you can release them to clear later waves nearly instantly.
Also yes, you got the principle of the 50% Rule correctly.