No, I do not fertilize, no reason to because they eat all the muck at the bottom including rotting leaves, dead bugs, duck poop, etc, etc.
I get in the pond several times a year and pull divisions out of the mud. This keeps the lilies 'pruned'.
Once you get hold of once of the running type tubers...it's like pulling up a thick rope. The muck is pretty loose so it doesn't take much pull.
I use a knife and pruners too, pulling and cutting/clipping at the same time. I usually have someone at the edge of the pond who catches all my divisions as I throw them to the edge of the pond.