I'm a T2 on a combination insulin and I low carb. I probably do about 50-60g/day on a weekday, but more at weekends.
I had a conversation with my DN last week at my annual review and we decided to keep a few carbs in the meals when I take my insulin as it needs something to work with when on a fixed combination dose. I'd not done well on the days when I'd dropped carbs from breakfast and had false hypos late morning. If you have mainly protein and fat at breakfast when you have your insulin, it might digest slower than the applied insulin works, so you can go too low.
So I have a slice of bread with my eggs, yogurt or whatever at breakfast, very few carbs at lunch and then a small portion of brown rice or potato with my evening meal.
This pattern works for me - and you will need to find the regime that works for you - it's very personal, there simply is no standard formula, and you'll need to establish for yourself which foods are most suitable to keep your numbers stable.
What I would suggest is to lower your carb intake gradually, if you're already on insulin you don't want to drop too dramatically, a gradual decline will make you feel much better as you go along and allow you to better assess what works for you. When I went on insulin, around the same time I started lower carbing, my DN said that it can take six months to get fully settled on it and find the right dose, type of insulin etc., so I knew it wasn't going to be overnight, so was prepared to invest the time into getting it right. I'll hit the 3 month mark next week and am delighted with the stage I'm at now, I'm just starting to actually feel properly better and my numbers are getting close to the ultimate targets we set.
So it can work really well on insulin, just take it steadily and test religiously.