It really isn't difficult to follow this diet and incorporate your animal beliefs, other then induction and early OWL. If you actually follow OWL quickly, or take an Atkins for life approach and start at 60g or so, you can easily be on plan. Eat Tofu, Tempeh (I love tempeh), lots of eggs (learn different ways to cook them), and loads of vegies.

A standard vegetarian very low-carb (early OWL) Atkins diet would be:

Breakfast: Large omlette filled with mushrooms (good for vege), spinach (iron - no red meat), and other choices.

Lunch: Salad made with lettuce, cucumber, vegies, etc with some pre-seasoned cold tempeh thrown in; or a marinated and stir-fried tofu for lower carbs.

Snacks: vegies etc, or try lower-carb whole milk yogurts later own; to keep fat content up try nuts, especially higher fat ones like macadamias; also to keep fat content up try roasting vegies that absorb a ton of oil like eggplant, or eat green beans or broccolli or cauliflower loaded with butter.

Dinner: Endless possibilities - I am actually not vegetarian but I eat vegetarian at least 3 nights a week.
Last night I got some squewers, (spelling!!), chucked on some cherry tomatoes, button mushrooms, green pepper slices, and tofu that I had soaked in soy sauce and garlic and chilli for a few hours, cooked in A LOT of olive oil. Chucked em on a fry pan, turned, dinner was ready in 10 minutes from start to finish.
Heaps of quiches, frittatas, etc in standard vegetarian cookbooks; some aren't that 'eggy' tasting if well seasoned
Try a big vegie roast (zuccini, eggplant, peppers) with a soy protein shake on the side.

Alternatively, if you want to stick to a lower-rung OWL band, which would require eating meat, have a long think about what your actual objections to eating meat are. Write down what your problems are, and think if there are animal products you could still eat for a while without feeling bad. I am thinking.
* Fish that is sustainably caught from the wild - not in overcrowded farms and not atlantic salmon (notorious!!) -- can I object to that? The fish live full lives, in the wild, not in there own filth etc. I mean, sure they die, but do I feel as bad about that as eating a cage chicken? It is easy to get such fish, ask your fishmonger. They may not know for sure if you live inland, but some web research can help you know what types of fish are in sustainable industries
* Game meats. I know many vegetarians that for health reasons reintroduced kangaroo (I am in Australia!) into there diet for health reasons. Find out how heavily regulated hunting is for certain animals avaliable is. Game meats that are hunted by businesses to be sold commercially tend to be very heavily regulated industries due to the risk of the disease etc. It also means the deer or whatever has lived in the wild, running up hills or whatever, rather then farmed.
* What about animals without nervous systems? Like clams and stuff? My old housemate was vege with this exception but I can't think what other things there are..
* What about, and maybe we are pushing it here, free range adult slaughtered chickens? Very easily avaliable.