The English words
LEMON and
LIME both come from Old French
lymon, meaning "citrus fruit" (including both lemon and lime) which in turn comes from Arabic
laimun, while the Arabic comes from Persian
limu (again with the meaning "citrus fruit"), which is cognate with Sanskrit
nimbu ("lime").
You can learn more about
lemons and
limes at Wikipedia.
The first image shows a
lemon tree with its fruit and flower, and the second image shows
limes on a lime tree: