I think one of the key conflicts you will need to figure out is dietary fat. A huge part of the vegan and vegetarian community has the belief that dietary fat of all kinds is unhealthy. And since you generally cannot or should not get more than 20-30% of your diet as protein, a low fat diet has to be high in carbs.
Personally, I believe that a wide range of dietary fats are actually very healthy and following a low fat diet conflicts with attempts to reduce the amount of dietary carbs. I actually think that as a vegan or vegetarian the challenge is not to find low fat carby foods, it is to find healthy high fat and high protein foods. If you eat eggs, then you shouldn't ration out one or two eggs a week, you should think about a couple a day. And if you eat yogurt, you should think about eating lots of yogurt and maybe even making your own. And don't forget the avocado.
But in the end, if you don't get your head around eating dietary fat, you will have a constant conflict that low fat diets are inherently high carb.