How would steam pressure move a lid?

The lid would lift up and vent the steam. It is unlikely that the pressure from the water vapour would be precisely the same over the whole area of the lid, so chances at that it would vent more at one side of the lid than the other. In other words, I think the square lid would tilt up in one direction or another, just enough to vent some steam along one edge of the pot. Once the pressure in the pot reduced sufficiently, the lid would settle back down onto the pot. Then pressure would build again until it was sufficient to raise the lid again, and the process would repeat.

If there was enough friction between the edges of the lid and the lid itself, then we would not expect the lid to slide around on top of the pot. It would just repeatedly lift and then settle back into position after some of the steam had vented. In practice, this could be like the lid vibrating up and down, possibly on more than one edge at a time.

So...

Why would it do that? If the lid is simply resting on top of the pot, then the pressure inside will never get much higher than it needs to be in order to raise the lid enough for steam to start venting. You're not talking about locking the lid down somehow, are you?

It would move up and down.

Up and down.

Yes, based on the pressure. It could depend a lot on how the water was being heated, too. Like, is the bottom of the pot being heated uniformly, or more in some places than others? That would certainly affect things.

Unlikely, unless there was very low friction between the lid and the top of the pot.

The pressure wouldn't get higher and higher. Venting results in a pressure decrease every time.

But yes, it would just lift along once edge at a time, unless things were completely uniform (which we wouldn't expect in a real situation). If, by some miracle, it was completely uniform, then the whole lid would lift vertically off the pot then settle back into position, repeatedly.

The lid wouldn't try to find "maximum exhaust". Any exhaust that relieves the pressure enough to allow the lid to settle back would be sufficient. Like I said, the most likely thing is that it would lift along one edge.

Unlikely, unless the friction was very low. If it was, then the lid could drift in any direction and expose either an edge or a corner.