No, I think you can separate them ok. Yes, leave the stem roots on. Plant the whole thing to where the stem roots are covered with several inches of soil, and then cut off the stems. Oh, I forgot, I mulch my lilies, keeps them cool in the summer and protects from temp swings that we have here in the south during the fall and winter. Despite that, my orientals always sprout the green tops early, sometimes at Christmas. I used to panic, but it doesn't seem to bother them. I still cover the foliage with leaves or a little extra mulch, though.
