"If you want to fertilize, put on a little well-balanced fertilizer at emergence time and about a month later. Slow-release fertilizers are also good. It isn't necessary to feed the lilies, though, unless your soil is poor and you want to raise super show-lilies. The sort of fertilizer that gardeners use in your area to grow potatoes will be fine. Too much nitrogen can produce lush leaves but weak stems, so don't overdo it. Heavy nitrogen in hot, wet areas can also set the stage for bulb rot. If you want to cut the gorgeous flowering stems, remember that the green parts are the food factories that are building up next year's bulb; if you leave the bottom two-thirds of the stem, it will easily make a nice bulb for the following year."
I fertilize when they are coming up with the kind that you already use. I supplement that with a balanced, time released fertilizer such as they suggest - Osmocote, the 14-14-14 three month kind.
I generally use a bulb fertilizer when I plant the, a liquid fertilizer at emergence, and Osmocote later. But as you can see from the above, they really don't need much.
I think they need a little extra help in my area. My Casa Blancas have gotten smaller every year and I was just on today to see what is recommended for fertilizing lilies. I do have some Osmocote and I think I will add some to them. I am also going to dig in a bit of mushroom compost too.
What you say about Casa Blanca is very interesting to me. Many years ago I took a White Flower Farm offer and got 12 for a ridiculously low amount. I put them right next to the house, behind some bayberries (where there is tons of gravel) and they thrived for years.
Then the bayberries got too tall, an I started moving them to locations around the yard. One by one they petered out. Last year I only had two left, so I put them in pots (I put dozens of lilies in pots, since I was moving). One basically keeled in the pot. I put the last one, as I did 70 other lilies, in zip lock bags with seed starting mix over the winter. Only one lily became a pulpy mess in the bag - Casa Blanca.
If you want something extremely similar , but with s a shorter stem, try Crystal Blanca, a relative of Casa. It is a lily I have had, and moved, several times over the years. It's tough, and a champ. I've had it since 2007. It is carried by B @ D Lilies. I have ordered from them for years.