I had hoped you would help me out by describing (or linking a photo) of what kind of filter you meant. OK, I'll do the work. Whisper makes hang-on-back style filters, like this:
http://www.aquariumguys.com/tetratec.html
and they make in-tank filters like this:
http://www.aquariumguys.com/whisperintank.html
It's quite illusive to me which of these someone would call "regular". And there may be other types also made by Whisper. Ian, I don't know if you had intended to link to a photo, or if you were being a smart alec.
The former type would be totally inappropriate, both because it won't work in 2" of water and because it allows gaps for escape. The latter type might work, but 2" of water might be too shallow for it. I'm not sure exactly what water depth it needs.
There are other types of filters that are designed to work in very shallow water, such as this
http://www.thatpetplace.com/pet/group/2587/product.web
or
http://www.thatpetplace.com/pet/group/12750/product.web
If you are serious about 2" of water, you need to shop very carefully for what will work. You also need to look for the least possible filter wattage, as this is correlated with heat production.
I haven't kept lucifuga, but I think you do just have to put pinheads or fruit flies in there and let him hunt them down. Both of these foods can be obtained in winter. There are several other kinds of live food that you can breed yourself, like woodlice or roaches. The problem will be that a lot of the food will drown before it gets eaten.