Nope, I haven't tried SuperSu on JLB. I wouldn't try things explicitly against original developers' instructions.
If the developer of SuperSU basically says - it requires a rooted phone, I believe he means it. The purpose of superSU is not to root a phone but to manage the root access of already rooted phone. Correct me if I'm wrong though.
Also, if you have any additional details on SuperSU, any hidden functions that root the phone - do us all a favor, please kindly share them.
Provided the rooting issues with JLB so far, barking at the wrong tree(superSU) won't help.
More deeper understanding what rooting is might do - su binary, busybox, a method to manage them and to take care of files' permissions. Unfortunately that is as far as I can help.