Limey is a slur used to describe British in a derogatory way. The British Royal Navy supplied a daily ration of lime or lemon juice to their sailors to prevent scurvy.
The word Limey is a racial slur that has been used historically to degrade and dehumanize british. The word is still used by some people for this purpose, and it is seen as offensive and hurtful to british. If you are unsure about whether or not it is appropriate to use the word Limey, it is best to err on the side of caution and avoid using it in any situation.