Regarding the Remon/Lemon debate, it's actually a really weird situation. In Japanese her name is written 檸檬 (れもん), so it is a Japanese word (with its own kanji and all), and therefore it could be argued that Remon is the correct romanisation. However, it actually does mean lemon, and (as far as I'm aware) is more commonly written in katakana (レモン), like any other loan word (such as bagu = bag, orenji = orange, etc). So frankly, I don't think there is a right way to translate it, and either Remon or Lemon could be considered correct. Personally I lean towards Lemon, since it retains the original meaning of the name, whereas Remon doesn't mean anything to an English-speaker.
Yeah, I know it's a silly thing to waste time worrying about, but I think it's kinda interesting. One of those odd quirks of Japanese that seem to exist for no other reason than to confuse people.