Veganism is just too restrictive for Atkins. You would be eating way too much carb from the vegetable and soy-based diet.
Here are my meal plans for following a lacto-ovo vegetarian Induction.

You'll want to choose carfully from the below options, which will generally keep you in the 20-grams of carbs per day limit required of Atkins Induction. (PS-I trust calorie-count.com for all my nutritional info.)

Breakfast
Option 1: 1/2 of an avacado with 1 tbsp chopped tomato and combined with a pinch of citric acid (available in most health food store spice isles) mixed with 2 tsps of water and served on a thin slice of tofu that has been well drained on paper towel and then sauteed lightly in veg oil or butter.
Option 2: Soy protein isolate shake with vanilla or coconut flavoring and a 2:1 ratio of cream and water (sweetened with 1/2 packet of splenda). It's actually very good.
Option 3: 2 fried eggs and 2 rashers of Fakin Bacon (tempeh strips), half serving of Atkins Zucchini bread, de-caff coffee or tea with cream
Snack 1/2 celery stick with almond nut butter
Lunch
Option 1: Homemade asian-style seitan stir-fry in a hot/sweet) marinade, and sprinkled lightly with soy nuts for crunch. Serve over 3/4 cup sauted mixture of sauteed bok choy cabbage (must be bok choy) and shaved celery strips.
Option 2: Morningstar Farms grillers, sliced thin and dipped in homemade spicy red-pepper salsa. 2 small cubes of soy cheese (about half a serving), 2 asparagus spears, 1/2 cup zucchini, or green beans.
Snack
Option 1: 1/3 cup red pepper strips, 1/3 cup cubanelle pepper, 1/3 cup cucumber, mixed with homemade white vinegar, Splenda and citric acid vinegarette.
Option 2: The above, but decrease to 2/3 cup, and dip in 2 tbsps of low-carb ranch dressing.
Dinner:
Option 1: Typically, just a big vegetable salad (about 2 cups), mixed with boiled egg, seitan, tofu, or other low-carb/fiber full meat alternatives, a cube of soy cheese if using an oil and vinegar dressing, otherwise I use a no-carb bleu cheese dressing. In the morning, I will sometimes cook up extra Fakin Bakin and crumble that on top with a few slivered almonds. Easy.
Option 2: 3 soups that are low-carb
1-1 cup of homemade thick and hearty spicy "blackbean" soup (made with 1/2 cup canned soy beans, mixed with 2 tsps onion, 1 tbsp celery, 1 tbsps chopped cubanelle pepper, white vinegar, chili spice and black pepper for flavorings, and vegetable stock as the base. Fills up and has a lot of fiber.
2- cups Mushroom soup made with 2 cups raw mushrooms sauteed in butter, 2 tsps diced onion, 1 cup cream and 2 cups vegetable stock or 2 cups water mixed with 1/3 cup vinegar (sounds gross, but works as a stock in a pinch). Thicken with soy protein isolate or with a very small amount of xantham gum.
3-Asian miso soup with tofu (any homeade or canned vegetarian-style will do, as it's typically very low in carbs. But be sure to check the label on any pre-prepared foods for hidden carbs).
4-Vegetarian egg drop soup using Asian-spice Vegetable stock, egg, and vegetables
5-The onion soup on Atkins' website, made with vegetable broth and gruyere cheese (for lacto diets)
Option 3:
Soy bean, seitan, or mexican-spice seasoned tofu "burrito", using a low-carb wrap and 1/2 cup fibrous vegetables, lightly sauteed, and topped with soy cheese. Use any of the Atkins-friendly seasonings you want.
Option 4: Chicken Tikka Masala
Top 1 cup grilled, seasoned chicken breast "grillers" (Morningstar Farm) with 1/2 cup crushed, stewed tomatoes, juice from 1 wedge of lemon, 3 Tbsps water or vegetable stock, 2 tbsps full-fat cream, spice mixture (to taste) of cumin, coriander, cilantro, garlic, paprika, salt and pepper. Serve over a 1/2 cup of "riced" bok-choy that has been sauteed in butter and tossed with toasted almond slices (buy pre-made or make yourself).

Snack/dessert:
Option 1- Atkins carb advantage protein bread that I will use for dipping into any of the soups above.
Option 2- A cheese course (if the food choices for the whole day permit it), served with de-caff coffee with cream
Option 3- The chocolate cream pots recipe in Atkins Essentials.
Option 4- An Atkins Advantage low-carb soynut bar. Some books say that the Advantage "dessert" bars are no-no during induction, I think it's okay, as long as you stay below your 20 grams of net carbs a day. Most of the dessert bars have just 2 net carbs.
Option 5- Cream cheese cinnamon tofu "cheese cake." I use this when I'm craving a quick sweet and my carb count for the day permits it. Note: this is for cinnamon lovers, but you can substitute your favorite baking spice, as long as it's Atkins approved.
Slice a 1/2" portion of tofu from the block. Drain and press between towels to strain all liquid from tofu. Butter both sides, and sprinkle very lightly with 1/4 tsp. of Splenda and sprinkle with cinnamon. Place on a pan in the toaster oven and toast on lightest setting, turning over to toast both sides. In the meantime, mix together 1 tbsp. of cream cheese with an additonal sprinkling (1/4 tsp) of ground cinnamon. Pulse grind 2 tbsps of soy nuts in coffee grinder until it resembles cornmeal. Place ground nuts in a pan over very low heat with 2 tsps of butter and 1 tsp. flaked, toasted wheat germ. Sautee gently over lowest heat until butter is incorporated and nuts and wheat germ are lightly browned. Remove from heat and sprinkle in a pinch of Splenda, mixing well. Spread cream cheese onto toasted tofu and top with the nutty mix, pressing it into the cream cheese. I usually enjoy this with a cup of black de-caff coffee while on induction. It has gotten me over some difficult periods when I was really craving something sweet and was ready to quit Induction altogether.