Lemon Battery Voltage Increase Suppose I have 2 lemons each with a zinc nail and a penny for electrodes and I wire them up in series so that Nail-A passes through a load and connects to Penny-B and Nail-B connects to Penny-A.
I think I understand that the lemon juice puts electrons into Nail-A as it creates zinc oxide and Penny-B is losing electrons as the lemon juice creates hydrogen gas and therefore a voltage occurs because of an excess of electrons on Nail-A and a deficiency of electrons at Penny-B.  I assume that something similar is occurring between Nail-B and Penny-A.
In the case of a single lemon, I can get roughly 1 volt between Nail-A and Penny-A.  But I get double that between Nail-A and Penny-B.  What exactly is the connection between Nail-B and Penny-A doing to increase the supply of electrons at Nail-A and therefore increase the voltage?
 A: I took the liberty of creating a diagram, illustrating the current flow.
Two Lemons:
<------Stuck together---->   <-----Stuck together----->
Nail-A---Lemon-A---Penny-A---Nail-B---Lemon-B---Penny-B
  |                                                |
  ------------------------Load----------------------

One Lemon:
<------Stuck together---->  
Nail-A---Lemon-A---Penny-A
  |                  |
  --------Load--------

If I understand correctly, your question is not about lemons specifically, or about the electrochemistry going on here, but about Kirchhoff's circuit laws, specifically the Voltage Law. It implies that voltages add up if you connect voltage sources in series.
In your case, two sources connected in series with 1V each lead to a "combined" 2V voltage source. 
This would happen with any voltage source, even mixed sources (e.g. lemons and oranges).
After looking at voltages, let's look at the current. Let's assume that the load follows Ohm's law and has a resistance $R=1 \Omega$, i.e. a 2V voltage drop across the load leads to 2A, a 1V voltage drop across the load leads to 1A. Because current is constant in a closed circuit, this leads to a change in the electrochemistry of each sources:


*

*1 lemon case: each lemon creates 1V potential difference, 1A current flows through it

*2 lemon case: each lemon creates 1V potential difference, 2A current flows through it


This "just" increases the number (happening in parallel) of electrochemical reactions as long as the current is low. With increasing current, other effects take over:


*

*The lemons themselves have non-zero electrical resistance, i.e. they heat up and "eat up" some of the voltage, leading to a decrease of the potential difference.

*The number of parallel reactions is limited (e.g. too little electrode surface or ions in the electrolyte). If the ions can't be transferred from one electrode to another as effectively, the current will still increase but the voltage difference lowers. An some point, the current increase stops.


Short circuiting the lemon would be the extreme case of the described situation. In that case, the output voltage drops to 0V (because there is no load) and the current is at the lemon-specific maximum.
The behavior at large (or maximum) current seems to be complex and there are quite a few results when you google it. The so-called Newman's model is used here and here.
I guess if life gives you lemons, connect them in series.
