Dhananjay V. Gadre wrote in with this awesome project:

We have been itching to try running an AVR micro on fruit power. I do
have the latest Picopower AVR samples, but it was too much of an
effort to solder a 64 pin TQFP and so we decided to give a try with
Tiny13V chip instead. The chip was setup to operate at an internal
clock of 128KHz with a divide by 8 setting. A program to toggle an LED
on pin 3 of the micro was set up with a series resistance of 4.7KOhm.
The fruit cell was made out of a bare PCB partitioned in 4 sections.
The copper of the PCB made up one electrode and for the other we used
zinc strips from new batteries :) Two lemons cut in half were used.

The setup works well and the LED light didnt seem to diminish at all.