There is a level very early on with two Kekes that requires you to push one over a river where water is sink. Seems pretty reasonable to me that movement would work the same way over lava. After all you’re not touching the lava during movement since it is at a lower height
That's different! Yes, when being pushed you're indeed not touching water or lava, but when moving, you do! So it's not obvious that the rules won't affect you in that case.
In none of the previous levels was it ever possible to move over water from one patch of land to another, so the only way for you to discover that 'sink' only affect you when you're stopped is to move 2 or more cells into water and notice that you sink when you stop and not immediately upon entering the water, but that detail is very hard to notice.
Given how not obvious it is that rules like 'defeat' and 'sink' don't affect units while they move, especially given that rules like 'stop' do, it's necessary to communicate this more clearly to the player. For example, on the second level, at least one of the mechs could start on a single cell island surrounded on all sides by water so that moving the mech off of the island was the only thing the player could do to progress.