1. obsolete A British sailor, so called because of the Royal Navy's practice of adding lime juice to grog in order to combat scurvy. Slightly derogatory. Primarily heard in US. A shipful of limejuicers just arrived into port where they met an icy reception from the locals.
2. dated By extension, any British person, especially a man. Slightly derogatory. Primarily heard in US. We don't need some hoity-toity limejuicer coming in telling us how to run our business. Why don't you go back to Brittania, you old limejuicer?
n. a British sailor; and British citizen, typically a male. (The first one is old. Both are a little derogatory.) Some limey answered the telephone and I could hardly understand what she was saying.