These guys are unusual for dorid nudibranchs in that they actually feed on tunicates, not on sponges (your LFS was actually closer to accurate about the diet than most I've heard of selling nudibranchs though).
They don't seem to terribly selective as far as which tunicates they eat, so these ones may potentially be able to be kept if you can grow out some invasive tunicates fast enough.
Since you likely don't already have a large amount of fast growing, colonial tunicates (which would likely require a healthy amount of phytoplankton to grow), though, I expect your nudibranch will slowly starve to death - sorry.
If you want to try and save/keep it, you can buy tunicates from a variety of places, but the only species I'm aware of that is sold at the moment that might be able to grow fast enough is the Golden Star Tunicate,
Botryllus schlosseri:
Order Golden Star Tunicate (Botryllus schlosseri) from Maine. A colonial ascidian specimen ideal for aquariums, classrooms, and marine biology labs.
gulfofme.com
Golden Star Tunicates are highly invasive, but they tend to prefer colder water - I can go into the specific methods of feeding and culturing these if you'd like, but it takes a few weeks for them to really start growing, and you'd need quite a large colony to provide enough food for your nudibranch long-term.
Anyway, for some more specific info on their diet and to see a number of different tunicates that they may feed on, see the links below:
The Sea Slug Forum - Nembrotha chamberlaini Nembrotha chamberlaini nudibranch Anilao