From the Super Mario Wiki
Lemons don't sell well anywhere and are largely only good for cooking. However, retrieving at least one is necessary for unlocking Dry Dry Ruins, as the way to earn the Pulse Stone (the only artifact capable of opening the Ruins) involves giving a Lemon to Sheek, who will then allow Mario to "meet" Moustafa (actually himself), owner of the Pulse Stone.
In Donkey Kong Jungle Beat, Lemons appeared at the end of every level in the Lemon Kingdom. After Donkey Kong reaches the end of that level, he munches through the whole lemon. This lemon is larger than Donkey Kong himself.