That is very interesting! I am also lactose intolerant! I use the lactase enzyme pills as well and they work good for me, except for on milk/ice cream, just like you. However, I buy lactose free milk at the store and that I have no issues with.
I have also recently come to the conclusion that I am allergic to something in eggs, as they make me gassy and often times will give me the ****s, but not until like 12hrs after eating them. I would wake up at like 4am and have to dart to the bathroom. Sometimes it would be every day for a week and then it would stop, but once I stopped eating eggs... No more problems. My breakfast options are so poor lol.