If you want it to live for longer yeah, wheatgrass needs full sun. You'll need a decent powered grow light to keep it going indoors as it's pretty sun hungry. If you just keep cycling new planters/pots, the wheatgrass seeds have pretty much everything they need to stay alive for fairly long, at least a month.

There is a number of issues with keeping it going, wheatgrass will eventually start growing more of a stalk from the bottom which is less desirable to your cat. You asked will need to feed it something heavy in nitrogen. Wheatgrass tends to come in a winter and summer variety as well, and I'm unsure what that means for long term growth. It's honestly a fairly finicky grass to keep alive.