It probably does burn. Between the flakes, the skin can be awfully thin - sort of like paper cuts or scrapes all over. Most creams have some alcohol in them. My husband says the Cetaphil is one of the things that doesn't sting too much, compared to a lot of other creams he has tried. Lachydrin is lactic acid. It eats away at the dead skin on the surface and makes the skin thinner. No surprise that it burns her.
Maybe the concentration of acid is too high for her. You can mix a little with the Cetaphil - 50/50, 25/75 or 75/25 - and see what is effective and if that doesn't burn as much.
IV seems an odd diagnosis unless either you or her father have it, too.
Ichthyosis-en-Confetti Type 2
Husband, Nathan - 10, Elliot - 7, Oliver - 4, all affected.
I also have an unaffected daughter, age 8.
email: jennifer at confettiskin dot com
facebook - find me on "ichthyosis mommy spot" or "friends of ichthyosis"