Can't you just tell them what you're doing..?

"I like to wander around campus a little during lunch to recharge. Thanks for asking though, maybe dinner?"

Just say you're busy / in the middle of something. Decline their offer enough and they'll eventually stop asking you. No hard feelings (I say this as the guy who often invites others out).

This is what I recommend too. If someone declines me politely with a reason like "Sorry I'm busy today, maybe next time." I'll probably wait a week or so and invite them again if I want to eat lunch with them. If they reply with something shorter like "I got something to do, sorry," with a less kind intonation I probably wouldn't invite them again.

Go occasionally, do your own thing most of the time.

"Oh, I brought my lunch. Sorry!"

I've been faced with the same dilemma. Eventually, I just started telling people "I have something important to do". After all, being on your own every now and then is something important.

You can also say you've got a previous appointment or engagement... which is also true, even though it's with yourself.

You must all be very popular people since you have to have a strategy to get out of doing things with others. Most people have the opposite problem. You'll seem very unsincere after a while though, if your strategy is to not tell the truth.

Is it that you don't want to hurt the feelings of others that you lie? It's a little immature.

Some good ones are you're saving money for whatever reason. Or you're trying to eat healthier and can't eat out as much.