Low carb vegetarian is indeed a challenge. I was a veggie for well over 12 years and gave it up for better health. Thats me.
Upping good quality fats are the first step. Real butter, cold pressed oils will help. Eggs are excellent so you have a good start. Plenty of fresh greens and veggies. This is the time to concentrate on as fresh as possible. The fiber will help and the vitamins are more likely.
Cutting down the starch will be hard. Consider raw nuts (not roasted), whole grains in their natural state (not refined) and sprouted grains. I am on the fence with legumes, personally I would rather have root veggies like carrots and yams before legumes.
I wish you the best in finding what works for you. Lowering carbs is always a good thing and moving towards real food is the best.