Calculation of the cell potential of a lemon battery experiment
I am afraid that nobody can predict the true potential of Zn/ Cu lemon battery. It is not a standard system. The electrode potentials you see in the published tables are measured or calculated under unknown or controlled conditions and one of the basic requirement is that the metal must be in equilibrium with its own ions.

The lemon battery, although looks very simple, it is too complicated to deal with.


When you insert the electrodes into the lemon, there are no metallic ions to begin with, i.e., the concentration of Zn$^{2+}$ and Cu$^{2+}$ is essentially zero. Just using plug &amp; chug approach for the Nernst equation will give you infinite potential difference. This is not what is experimentally observed.


1b. Even if we assume that some metal dissolves around in a few seconds, still the metal concentration is not high enough to allow a reliable use of Nernst equation.


Citric acid is not only an acid, but it has complexing/chelating property as well.
Any voltage which comes close the calculated potential from redox tables is a mere coincidence.


I think the proper way to determine the potentials generated by contact potentials. This is the realm of physics. Two dissimilar metals, when brought in contact, will generate a potential difference. See my previous answer Electrochemical reactions in a salt water battery