There are a number of different and sometimes contradictory claims that changing your diet (especially with regard to avoid meat) can have an affect on your sleeping pattern.
Here are a few related claims:
Juice fast reduces need for sleep - Source: Someone that Steve Pavlina, a self-development blogger, met at a party.
"if you're eating mostly raw food, you only need like 4 hours of sleep" - Source: Someone on VeggieBoards forum.
Vegetarianism can make you wake up faster and stay more alert, but not reduce sleep needs - Source: Someone on Let's Run forum
Vegetarianism can help you sleep more! - Source: Vegetarian Spotlight
Vegetarianism can help you sleep... umm... WHAT? - Source: Yahoo! Answers in its element.
Vegetarianism helped one guy sleep less - Source: Veganza blog
Another couple of anecdotes about needing less sleep - Source: VegFamily forum.
It's not in the top ten reasons bandied about to become veg*n (vegetarian or vegan), but it's definitely out there in veg*n circles. Generally, the belief is that becoming a veg*n gives you more energy with less sleep than eating meat, potentially because digestion of meat is difficult.