Protein most definitely is an issue. Your body needs protein. If you don't eat enough, it will start breaking down its own muscle tissue for it. Long enough of that and you start losing some serious muscle mass. Vegetarians can get protein from cheese, eggs, etc. Vegans have a harder time because they are strictly fruits, nuts, grain and vegetable. In that case, they have to make sure they eat enough daily protein in the form of legumes (like lentils and other beans), tofu, etc.
In addition, hemoglobin (or hematocrit) plays a big role in sports like cycling. That's why EPO is so popular in the pelotons. This means red blood cells. In order for red blood cells to be produced, you need sufficient levels of iron and vitamin B12. You can't get much of either from a strictly vegan diet (vegetarian not so bad). Both vegan and vegetarians usually need supplements for iron and B12. You can get iron from dark leafy vegetables, from raisins, and a few other things, but you cannot be a vegan or vegetarian without knowing what you're doing, because you need the supplementation as I said, plus you need to eat the right mix of non-meat proteins in order to get complete high-value protien. If you don't it doesn't take long before you start feeling and looking rundown. If hematocrit drops, it doesn't take that much before you start feeling it in your cycling.