It's not terribly important so long as your vegetarian diet is balanced and healthy. Lean meat is a very good source of protein but in many cases the meat people consume is fatty and prepared in an unhealthy way.
Many people might also have ethical concerns with the meat industry as to how the animals are treated and concerns with steroids, antibiotics or other chemicals in the meat.
Bottom line in my point of view is that if you like meat, stick to lean cuts & preferably grilled, make sure you also get your fresh fruit and vegies. If you don't like meat or just don't want to eat it, that's fine as well and there's no reason why you can't still be fit, healthy and achieve an attractive, athletic physique.