With the release of version 6.2, Titanium Backup should now play along nicely with Android 5.0. This means rooted users who have already jumped to Lollipop can continue to use the tool to back up, restore, or freeze whichever apps they wish.
When you install the app, it's not going to look pretty. There's no Material Design to drool over, nor are there any fancy animations to catch your eye. Even the icon looks a little out of date these days. But this is Titanium Backup, and that's just part of its charm.
The developer has also quashed some other bugs, so give the changelog a glance as you go to try out the app. Just keep in mind that 6.2 comes with "initial support," so while things should work just fine, there's always room for surprises.