I read all kinds of things that said the milk will scorch if it gets above 70-something degrees. While it may cause problems for some people, that has not been my experience. I have gotten my milk/lye solution temperature as high as 110 degrees and have never had a batch scorch. I also read that gelling milk soap will scorch it. Acting on the advice I got here on the forum, I have been intentionally forcing gel in all my soaps and have never had a scorching problem.
While it is always important to follow safe handling procedures, I think that sometimes it doesn't hurt to push the envelope a little and try something outside the "norm" and see what happens. The result might not be as bad as you think! I might get brave and try adding the lye like you did and see what happens. I'd sure like to find a faster way to add lye to milk. Adding it slowly all at once, and then stirring every few minutes would be a lot less time consuming than the way I'm doing it. I could use that time between stirring to weigh fragrances, set up molds, mix colorants, etc.