I'm not sure if you would need to book a special meal to stay low-carb. I have only had one F experience cross-Pacific, but on that flight you could chose your main course and your vegetables separately. So, you could chose steak plus grilled eggplant, and not have to worry about starches. For breakfast I think you could chose eggs and sausage - again, should be ok from a low carb point of view.

Enjoy your flight!