Hi. MY son is 3 years old and has LI. In the colder weather, he pretty much scrathes constantly. Since itching causes little breaks/tears in the skin, ALL of his lotions, etc. burn terribly.
I have found that keeping the scales removed as best as possible and keeping the skin moist does help. He happens to be in this phase where he doesn't want to be lotioned. I am trying to convenience him he needs it, but that is another story all together.
Anyways, I have found that using some sort of oil (baby oil gel, almond oil, jojoba oil, etc.) really helps. We use mostly baby oil gel due to cost. I apply that all over from head to toe (it works great for loosen the scales on the head). Then, I apply shea butter as of now. It is the only thing that has yet to burn. I buy the NOW brand from Whole Foods or HEB. It is between $8 and $10 depending on where you get it.
My sitter will then put him in tight clothing such as long sleeve and long pant pjs. This really traps in the moisture. Plus, what kid doesn't love staying in pjs all day? The added plus is that you are not ruining the elastic in the everyday clothes as quickly. Though she has begun using some of those as well. Not very happy with that one, but what do you do when they take absolutely the best care possible of your kiddo. She is a blessing to our family.
Now, if I do not want to deal with the greasy mess, we use eucerine calming cream (he says it burns where he has scratched), aveeno itch relief, or gold bond with shea butter.
Gold Bond is our favorite cream thus far for anytime of the year it has real staying power. Others we like are Curel Ultra Healing and Jergans She Butter Lotion.
We have to alternaate when his skin gets use to it.
I do use sea salt and oil in the bath water to help soften the skin. Walmart now sales a tub of sea salt near the lotion that is about $5. I use at least half of the container in a tub of water. Using the whole container does work better though. We have been using skin so soft from avon in the bathwater as well. It is VERY SLIPPERY so be careful to watch the little one closely. I have slipped a couple of times even after washing out the tub.
Hope this helps in some way. Unfortunately, trail and error is something we get use to when seeking comfort for those we love.