In my language (afrikaans) we say fruit are green if they are unripe. Even if it is literally not the colour green. I imagine the same principle applies to Italian.
Come on....all clever explanations aside...a lime is green, a lemon is yellow. An unripe lemon is green yes, but then you have to say it is unripe... :-). In french a lime is called a green lemon so maybe the solution lies therein!