Yes, if you make a lemon-based battery, it is the acidity of the lemon that causes the electricity to flow. You may have also heard of making a battery out of a potato. This works, but since potatoes aren't as acidic as lemons, lemons work better.

The exact details can be tricky, but in short, the acidity of the lemon makes it a lot easier for electrons to flow from the Zinc to the Copper.