You can have it wet and still be firm enough to have a layer of 1/16" on your face. That's just a guess on thickness. As long as it's not see-through it's thick enough in my opinion for a straight. The quality of soap makes a huge difference with this too.
I'm far from an expert with a straight razor. I'm using shavettes and I had a lot of trouble with a wet lather that has a lot of surface water in it. I've found that I like a thick, cushiony lather. I've also found that that's what I like with my DE and GEM razors, too. I figured it was just a YMMV thing and that ended up being what my face likes best.