As a sidenote, I have looked into low-carb/keto diets and I've found that those are rather hard for vegetarians; reducing carb intake from some sources (rice, pasta) is easy, but even staple vegetarian foods rich in protein (tofu, lentils, beans, quinoa) are 1:1 when it comes to protein:carb content.
Another thing to mention is that being vegetarian in a central European country limits you to a very few number of restaurants you can eat out with friends; I do not know of any place around that would serve vegetarian low-carb food. This would imply that I always bring my own food from home to work, socially exclude myself by not eating anything when we go out eating with friends, and so on.