I have a lily that's been here only about a month, and it's already rooting outside the container.
I cull mine every other year. How big is the pot that it's in? The pots they sell them in are generally not the best pot to grow them in. I use either oil pans (thanks to
@addy1 for the idea!) or dishpans. Something shallow and low is better. They do make lily pots - shallow, no holes - but they tend to be more expensive. Although I did pick a few up at one of the big box stores a few years ago and they weren't too bad - maybe $5 a piece.
The idea is to plant the tuber so it can grow across the pan. I put mine with the growing tip near the edge and the tuber pointed toward the middle. In a larger pan, I'll put two in across from each other. In nursery pots they tend to grow up and out instead of staying in the pan.
Here's the oil pan:
Here's a dishpan:
And here's an official water lily pot:
As you can see, all serve the same purpose - contain the lily while it grows! A good lip on the edge is helpful. I use a garden rake to grab them and pull them around or out of the pond when I don't feel like getting in (aka the water is freezing!)