Juice is fine, and juice you make yourself is better than what you buy, but it's only part of a complete diet.

I find it hard to beleive that people will die without eating meat. Having poor nutrition on a vegan/vegetarian diet doesn't mean that they will die without meat, it means that they have a poor vegan/vegetarian diet. Of course it's more effort to get all the required amino acids on a vegan/vegetarian diet, but it's not impossible or even terribly difficult, if you are willing to do a little research and change your diet.

But being vegetarian/vegan in itself isn't going to make you a faster cyclist.