Atkins turns out to be perfectly healthy, based on huge long-term comparative studies matching it to other diets like Zone and Ornish (low fat), with the caveat that it is only healthy if you confine your eating of a high fat diet to times when you are keeping your carbs below about 100 g a day.
Where people get into trouble, long-term, is that they learn to eat a high fat/high protein diet but then they let their carb intake climb until they are eating 150 g a day of carbs, but they keep eating that extra load of fat. Fat and carbs are a toxic combo.
So just think of there being a slider between carbs and fat. The more carbs you eat, the less fat you should eat, the less carbs, the more fats are fine. To be really healthy, avoid all trans fats and the vegetable oil fats. Butter is actually a lot healthier than most vegetable oils, though this is not what the public has been taught.
Personally, after many years of watching people attempt to sustain very long term low carb diets at levels low enough to control diabetic blood sugars, I would say that trying to do a vegetarian low carb diet is setting yourself a near impossible task. The people who I've known who succeed at low carb living eat a lot of cheese, meat, fish, and fresh low carb vegetables, with a small amount of berries for fruit.
I would also caution you to be very careful to avoid getting the protein you need from processed soy products, as there is quite a bit of evidence they can both damage your digestive tract causing autoimmune problems and slow the thyroid. Soy can also cause hormonal and mood imbalances. I have experienced that myself and have talked to other people online who had the same problem when they were eating too much soy cereal and soy protein powder.
But as I say, cutting carbs safely and in a way that leads to long term health is a complex topic and one you really need to read up about. There is quite a bit you need to understand to do it properly. I ate a very low carb diet for more than 7 years to control my blood sugar and experienced nothing but positive health outcomes, but I did burn out on the foods that I was limited to eating. Eventually I raised my carb intake a bit to about 120 g a day and cut back on the cheese and fatty meats. That gives me a much wider selection of foods to choose from. But I still eat only what I can eat while keeping my blood sugars in a healthy range.
I don't eat any prepared, processed boxed, canned or frozen foods and I stopped eating trans fat and high fructose corn syrup back in the 1990s when the online diet community first became aware of how dangerous they were.
But I have seen an awful lot of people try to invent their own low carb diets without reading up on the principles of how the diet works, and they often end up going astray. So do read up. The Atkins books are a good starting place, if you can ignore the circus barker tone and the iffy research he cites. You won't go wrong eating the way he describes and there is much better research available now, a decade later which lays out more of the realities of the diet and how well it works.
Personally, I believe its greatest benefit is in how it controls hunger due to fluctuating blood sugars. Many people have abnormally high blood sugars too low to register on doctors' screening tests but high enough to damage their cardiovascular system over time and to make them feel hungry too often.
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