I actually just got a JL juicer recently as a gift and this is the first time I'm using it on the cleanse. It works fine really. I cut the lemon/limes in quarters and just hand peel the skin off the back. It seems a liiitttle less sweet than usual because of the white part that gets left behind. I like this better as before my hands would ache after juicing all that fruit! It pretty much takes the same amount of lemons and the same amount of time (maybe a bit quicker though). And the juicer is relatively easy to clean. I say give it a shot. If you don't like it, go back to hand juicing. That was my plan and the JL juicer won out. Good luck.
By the way, have you juiced wheatgrass with the JL juicer yet? It says you can, but I haven't tried it.