I have done over 20 LFs in the last 3 years and have done them at the end of a 40-28-21 day MC. After my first MC (40) from lack of knowledge I did it on the last day of the MC and had no problems at all and it was very productive. I passed a huge 3cm boulder. I don't think it was solid chunk. It looked more like a cluster of smaller ones.
As I proceeded on my cleansing quest I read that it's best to gradually introduce fats for around a week after the MC to let the system build up some bile to have a more productive flush and that's what I have done and will do when I finish my current 40 dayer.
I have always used the Clark protocol using Grapefruit juice to mix with the epsom salts instead of water. Pink grape fruits are the sweetest and kill the acrid taste of the Esalt best.