@SarahGen-- I wonder if you can mix lemon juice with something like honey to avoid those reactions. Honey is also great for skin and it's soothing, so I think it will prevent the lemon juice from causing itching and stinging. I don't know if it will be as effective, but it's probably better than nothing.
I use lemon juice on my skin all the time and I've never had problems. I take a lemon, cut it in half, turn it inside out and use it as a scrub in the shower. I first use it on my face for my freckles and then the rest of my body. It lightens and brightens my skin.