A key aspect of low carb is eating a ton of healthy vegetables and healthy fibers. This means that low carb can work quite nicely with a vegetarian diet.
First, let me point out that the idea of being a vegetarian has been corrupted in modern times. Vegetarianism has traditionally been about eating a very healthy blend of fibers, nutritious vegetables, non-meat proteins (soy, etc) and dairy products to give your body the nutrition it needs without harming animals. However, many modern eaters end up eating a ton of white pasta, white rice and bread with NO nutrition at all, and then add in sugar-added jelly, sugar-added peanut butter and junk food. That is about as 100% against what vegetarianism is about as you can get. You're supposed to be doing this to help make your body more healthy and to stop from harming animals - not to fill your body with junk to support junk food makers :)
So really, a nutritious vegetarian lifestyle and a low carb lifestyle intersect almost completely. Many low carbers focus on healthy grilled meats as their "protein" - so grilled chicken and salmon. If you were a semi-vegetarian that ate fish, you'd be all set. Just use salmon, tuna, mahi-mahi for your meat courses and you are perfectly set. If you are a true vegetarian that doesn't eat fish, you would go for the traditional protein substitutes - eggs, soy, chickpeas and lentils, whole-wheat products.
It is important to remember that nine amino acids are *critical* to human healthy life and must be eaten daily. Your body does not store up protein. While meat naturally gives you what you need, most non-meat products provide only a few of those amino acids. Soy does offer a complete amino acid set, but there are problems with soy and fertility and other issues. It's important to understand which food items hold what amino acids and to balance your diet. Be sure to talk with a physician before you embark on a vegetarian diet, to ensure you do not end up with a serious deficiency based on your meal plans.