There really isn’t much in the way of icemelt that won’t harm your lawn, especially once you get much below about 25F.
There is a reason that we used so much sand back East. I mean, you don’t have to melt the ice if you can still drive over it safely without skidding, right? And sand may make a mess, but it works in all temperatures and is non-toxic. Best of all, it’s pretty damn cheap.