CJ,
An interesting topic question. First, you ask is it possible to create Lichtenberg figures in a science fair experiment?
The modern 3D type inside of a solid non-coductor such as acrylic is probably beyond your reach, simply because is it normally done using a linear accellerator to fire electronics at speed very close to the speed of light.
However, the old fashion, surface discharge figures are much more easily prepared if you have access to a static electricity generator. Your school science lab may have one. Or, if you are ambitious, you may build or buy one. You will need to build up and store a charge, then discharge it onto the surface of a non-conductive surface such as a white acrylic sheet.
Have you performed a web search on the subject? I found this site to be useful:
http://en.wikipedia.org/wiki/Lichtenberg_figure
The classic method of viewing the electrified regions was to use sulfur and red lead powder sprinkled onto the surface, then gently blow away the excess. I wouldn't recommend the use of these powders, especially the lead, as it is toxic. However, in these modern times we have access to something specifically design to show such electrified regions that is much safer, xerographic toner. This black powder is comprised of tiny beads of polymer that are easily attracted to charged areas... which is how they work inside of a photocopier, being attracted to the areas of the photoconductive plate that were NOT exposed to light reflected and focused from the paper to be copied. You won't need much of the powder. You can probably get enough from a used cartridge or two, keeping the cost of your experiment low. Just ask the school administration office to save them for you.
Oh... and you might want to wear old clothes and keep some cleaning wipes handy... that powder is messy!!! It may take a bit of experimenting with the procedure to get good results.
IMPORTANT SAFETY NOTE: Wear a dust mask over your mouth and nose. Do not breath in the powder. All powdered materials can irritate the lungs.
Good luck with the experiment !