Lilies grow in pots well. I haven't found baking to be much of a problem (and I'm in Maryland). While I don't let my pots get real dry for long you have to be careful not to soak them constantly since lilies are susceptible to rot. The bigger problem is overwintering them - since they aren't as insulated from wide temp. swings as when they are in the ground.

Instead of putting different types of lilies in one pot, I'd use 3 pots arranged together and rotate the in bloom pot to the front. Depending on your arrangement the others should still get enough sun to feed the bulb. I'd worry that planted together I wouldn't have the flexibility I'd need since lilies grow to very different heights.
-Helen