I have LI and I can barely sweat. Sweating in my case only works on my nose, my palms and the soles of my feet. To my understanding many of us can not sweat at all or only in certain areas. I do not know what influence the type of Ichthyosis has on the ability. As a child the inability to sweat was a big problem because teachers and other grown ups had a hard time telling when I was about to overheat (or they simply did not believe that I can not sweat), which naturally happens if the cooling system of your body does not work.
All the best,