Lemon juice contains electrolytes, which can carry electricity. It can't produce electricity by itself, but it can allow two different metals to react with each other. We call the reaction a redox reaction, which is short for "reduction and oxidation." One metal gets reduced (gains electrons), while the other metal gets oxidized (loses electrons). These names are a little confusing, because "reduced" makes it sound like the metal is getting smaller, but it's not. And "oxidized" sounds like it is getting attacked by oxygen, but the process does not actually require any oxygen. (Oxygen does tend to oxidize metals: metal oxides form when an oxygen atom steals an electron from the metal, forming a strong bond.)

Lemon juice contains citric acid. Because acids break up into charged anions and cations when dissolved in water, they conduct electricity because the charged particles are able to flow within the acid.