I'm no expert for sure, but I will tell you my experience with it. I followed the Brewer Diet (Dr. Tom Brewer, Blue Ribbon Baby) during pregnancy, and it is very high protein and relatively low carb. I stayed on it for the first three months of my son's life, and my milk supply was great! I started Weight Watchers when he was about 3 months old, and even with the extra points given for BFing my supply tanked. I stopped and went back to eating basically the same way I did when pregnant and my milk supply went back up. He weaned right after his 3rd birthday.

I wasn't trying to be LC, I was just trying to avoid any pregnancy complications and grow a big, strong, healthy baby, but in hindsight it was a very healthy way to eat and very low carb by default. He recommends so much protein that you don't really have room left for any simple carbs.