I don't know about in the kindergarten classroom either (I use it with 7th and 8th graders). However, it teaches them responsibility and who can say you're too young for that (OK, too young if you can't talk and communicate your feelings, but even babies can benefit from L&L).
I am a mom of a 7yo and 3yo. I started L&L when the 3yo was a baby and 7yo was 4. They responded well to it, and still do.
You would be amazed at how even young ones can come up with solutions to the problems. Just last night, my two sons were fighting and not going to sleep (we're in a temporary situation where they are sharing a room and it's not going that great). I took the older son out and problem solved with him (Looks like you've got a problem! What have you tried so far? How has that worked? Would you like to hear what other kids have tried?). Then I took the younger son out (who was really causing the problem--he does not fall asleep as easy as the older one and jabbers on keeping the older one awake). I told him his talking and getting up and playing was causing a problem for his brother and I. He hugged me and said sorry. I said, OK, but how can we solve this problem? I totally expected to provide all of the choices for him because I didn't think he could come up with any on his own. Boy, was I wrong! Here are the choices he offered with no prompting:
1. Sleep in another room
2. Sleep with Grammy (we're staying in my mom's house due to flooding)
3. Run away (I, of course, took that one off the table)
I thought that was pretty good for a 3yo!
For 5yos, I would probably use a lot of "Would you like to hear what other kids have tried?" I also LOVE the CD
Quick and Easy Classroom Interventions from the L&L site. It has lots of elementary examples on it, including how to get kids to wear their coats during winter recess!

Another good resource that has elementary stories is the book,
Creating Classrooms Where Teachers Love to Teach and Students Love to Learn.
I hope you give L&L a try. I love it, not only because my classroom is peaceful and productive, but also because I feel I am teaching my students life lessons that will really help them to be successful in the future.
Jenny