If you can do vegetarian and not vegan (meaning that you still eat dairy products and maybe eggs) you can still go low carb and have all the benefits.

For sure you cannot eat Induction level carbs and stick to a vegetarian diet, but you could certainly eat like you are in OWL or Maintenance, and it will still be healthier than a high-carb/low-fat regime, IMO.

Non-flesh sources of protein that work for me (I only eat chicken and only every second day) are:
almonds
natural peanut butter
tofu
sour cream
heavy cream
cheeses of all kinds -- hard, soft, cream
eggs, eggs and more eggs
chickpeas
blackbeans/turtlebeans

Also, to supplement grains, I use things like dreamfield's pasta and low-carb wraps (sparingly).....it is easier to eat vegetarian Atkins this way, but it can have it's consequences (some people can't handle the low-carb products).

It really depends on what your goals and priorities are. If you are willing to sacrifice faster weight loss to not consume meat, then I think a low-carb Atkins that uses the higher-rungs of the carb ladder works best. It will be slower going, but you can still reap the health benefits and weight loss over time.

If you want to go full-on vegan, however, it is very difficult to stick to a low-carb plan, since all the protein options left to you are high-carb and usually low-fat.

In DANDR there is a blurb about vegetarian Atkins, it is worth a look.