Really not a good idea. Your body needs that fat as a buffer for breastfeeding. Eat good quality food, fruits, veges, lots of water. What you feed yourself is also what you feed the baby, so eat good stuff!
I breastfed while doing IF and lost lots of weight, but instead of being thick and fatty my milk was closer to water. If you do decide to move forward with it, I’d recommend substituting with formula so your baby is getting all the calories and nutrients needed. I was also highly discouraged from doing it.