Hello! I stumbled across your question and though I'm not sure about charged water helping with lymphedema, I do know that juicing organic fruits and vegetables could very well help it.
If you go this way, try to avoid starchy vegetables at first, like carrots. Try a juice concoction of celery, watermelon, cucumber, Kale, apples, lemon (with a small amount of rind), and asparagus. If you don't have a juicer, a blender will work. Just strain the juice out of the pulp using cheesecloth.
I would recommend you drink at least two, 8-ounce glasses per day to start off, and eliminate all dairy and processed foods from your diet, and limit meat consumption, if not completely eliminate it. Increase fiber intake (you can use the pulp from your juicing to make yummy garden burger patties by juicing the kale, asparagus, and apples before you juice the watermelon to keep the pulp separated for the burgers. Also try and remove as much of the hard, bottom part of the asparagus before juicing it). Eat lots and lots of fibrous fruits and vegetables, and drink at least 64 ounces of water per day (it sounds like a lot, but it's only 8, 8-ounce glasses). Use sprouted breads and try to limit all white foods and coffee products.
You may start feeling better within the first week, depending on how clean you've kept your diet, but it might take a few weeks before you notice any real changes.
Please let me know if you have any questions, or if you do it. I'd love to hear your results!