There is "Italian food" by the North American definition, and then there is the food what Italian people who live in Italy actually eat. For example, not too many people who live in Italy are going to be eating a 4000 kcal bowl of Fettucine Alfredo like you see on offer in North American "Italian" restaurants. Same goes for the lasagne, pizza, spaghetti with meatballs, etc. They just don't eat that kind of thing as a rule. Italian people are very concerned about their weight and their appearance in stylish, fashionable clothing.
A woman named Viana la Place has done a lot to bring cookbooks of real Italian food to the english speaking world. Of course, her books are not "low-carb", per se, and do contain pasta and bread sections, but they are also full of many other recipes that are low-carb in nature. I highly recommend her cookbooks. Cucina Rustica is a very good first starter:
That's not an affiliate link, either, just my opinion that this is a really good Italian cookbook written in English. I've owned it for 20 years, and I still refer to it now and then.