You could still be vegetarian and do low-carb and low-sugar.
I mean, chocolate is vegan, coconut oil is high in fat... on the raw side, avocados and nuts also have a high fat content, especially if not eaten in moderation. You could very realistically do low-carb and low-sugar as a vegetarian. Everything in moderation. Disclaimer: I'm biased because I'm a pescatarian (vegetarian except I eat fish because omega3's and yum)
t-t-tell your boyfriend, if he says he's got beef,
that I'm a vegetarian, and I ain't f***ing scared of him
love is the best diet