Live oak can be got in the piles here in Charleston, SC. Yes, it's basically Red oak and it does tend to bend and split a lot. If you're good at turning really thin, green wood, you can make some bizzare shapes on it if you steam it a bit (wet it down real good and nuke it in the microwave a couple of minutes to make pliable) and use some clamps to bend it to the desired shape, but don't go too harsh. When it dries it should stay that way.
Drying by soaking first in denatrued alchohol will help with reducing splitting and maybe with the amount of warpage.
Anyhow, just know that live oak is very, very susceptible to "heart rot" where the pith of the tree basically is like wet rotted mud. Often stinks, too. But you'll see it very quickly upon chainsaw surgery--- you may be able to use it as a funky "natural edge" bowl.
Good luck.