Lilies like shallow containers, but they also grow in deep ones. The tubers stay on the surface. You could plant 2-3 in that pot more if you want to, eventually you will need to repot and space them out. Two feet under the water is a good depth. Mine are anywhere from 1.5 feet deep to 3 feet deep. I keep them out of the 5 foot deep area.
I use the walmart oil pans. They are 15 inches wide. When the lilies grow well I can end up with 5-6 tubers in the pot. The only real issue is when the leaves head to the surface they tend to bunch up, push out of the water. Lilies have a leaf spread of 3-8 feet ( estimate) Mine all tend to take up a circle of around 5 feet. I have some that are space hogs they put out a lot of leaves. Some that use less space.