I know this is a little late, but i've been working with LS for goat milk and through trial and error I've found a few things out:
It only works well with the CP method. HP burns the milk, and with the KOH already trying to cook the milk during the lye to liquid stage, you don't want to over cook it any more than you have to. That being said...
FREEZE YOUR MILK! Doesn't matter what kind. Freeze it and slowly add the lye to it that way, letting the lye melt the milk. You're less likely to burn it that way. Then once it's all melted and incorporated, cover and put it in the fridge, or an ice bath, to further cool the mixture. Then go about your soap making process, again, using the CP method. Be aware, that neutralization may need to be done using Borax, or you can let it sit and "cure" like with solid soaps.
If you do burn it, the ONLY thing I've found to help "mask" the smell, is Honey and Oatmeal Cybilla FO from Brambleberry. Something about that scent, and the burnt smell, just mesh. As for "fixing" the burnt color, Kaolin clay might help, but it will cause a lot of slip in the tub. You can also try a white irridescent powde, or Zinc or Titianimum Oxides.
If anyone has anything to add to this, or correct me, please share. Cause I'd love to know myself.