The lemon cell consists of two dissimilar metals
(copper and zinc) pushed into a lemon
and joined by an external wire.

This cell does not make a good battery as:
there are no copper ions for the half reaction:
Cu²⁺ + 2e¯Cu
to occur at the positive electrode.
The reaction at the positive electrode is probably:
2H⁺ + 2e¯ H₂

While the reaction: ZnZn²⁺ + 2e¯,
could occur at the zinc electrode,
the acid of the lemon could also react directly with the zinc:
Zn + 2H⁺Zn ²⁺ + H₂
Thus both electrodes become covered with hydrogen bubbles
and the cell quickly loses its potential.