Sometimes people go into way too much detail about why they can't make something. This would work fine:
"Sorry, I won't be able to make lunch. I have an important meeting that came up last minute."
Being nice, you might add:
"Sorry, I won't be able to make lunch. I have an important meeting that came up last minute. I really wanted to make it – I'd skip this meeting if I didn't have to make it. I'll make it up to you…"
Something along those lines – letting the other person know that lunch was important to you and that you aren't just snubbing them – seems well called for. But sometimes you get:
"Sorry, I won't be able to make lunch. I have an important meeting that came up last minute. I really wanted to make it – I'd skip this meeting if I didn't have to make it. We're weren't supposed to have it – the whole deal was off the table but then Jim got a call from the guys over at More Important Than Lunch, Inc. and they suddenly want to discuss it again. So Jim calls me and is like, 'Chris, we're talking to them in 15 minutes.' And Jim's really concerned because More Important Than Lunch could like bring in so much revenue and . . ."
And what was an apologetic explanation turns into a detailed description of just how important/interesting the "Other" thing is. It's another way the fact that people like talking about themselves trickles into typical situations. We've probably all done it.