The basic purpose of this experiment is to demonstrate the generation of electricity via galvanic action between two dissimilar metals, using some form of an electrolyte - which, in the case of a lemon, is the acid of the lemon. Please see this table:
Note the column "EMF (Volt)" - this is something like a "galvanic voltage level" - basically, you can pick a couple of metals from this list, and the difference in the voltages is your "generated voltage". So - for copper, it is roughly -0.2 volts, for zinc it is -1.10 volts, and for magnesium it is -1.6 volts; so, the maximum voltage between the two most commonly found metals (copper and zinc) is about 0.9 volts (1.1 - 0.2).
So - what you want to find and use for your electrodes is something made of these metals, and for best action , they should have a lot of surface area to contact the electrolyte.
You can easily find everything at Lowes - the people there are just idiots.
For the copper - go over to the hardware section; you can either use a piece of sheet copper (alternatively, you could use brass - but your voltage will be lower; see the table), which can sometimes be found where the sheet metals are located at.
Another (and easier to find) source of copper would be copper water pipe. You could make a strip by cutting a section of pipe off with a hacksaw, splitting it lengthwise, bending and hammering it flat, then cutting a strip off. Not easy, but doable. But bear with me - I'll show you something.
For the zinc, you have a couple of options: You can use hot-dipped galvanized steel - you'll find bolts and nails like this; a bolt would probably work better, as it exposes more surface area (for a somewhat thick bolt), but in a pinch, a nail could work. Hot-dipped galvanized steel is grey and rough - very ugly, because the steel part is literally dipped in molten zinc and allowed to cool. Alternatively, you could use galvanized sheet metal; this has a shine to it, but not like non-galvanized steel. Go look in the heating ductwork area; steel heating ducts are made with galvanized sheet steel. You can also find sheets of galvanized steel in the hardware area.
Another source of zinc is from what is known as "sacrificial anodes" - which are pieces of zinc that are used and placed inside steel and steel-lined swamp coolers (evaporative coolers) to keep the unit from rusting out. You can usually find these parts where the coolers are, but unfortunately, it is wintertime, and all of that summer stuff has been put away...
Lastly - you can get zinc from a old carbon-zinc dry-cell battery (a "D" sized cell will give you the most) - whatever you do, DO NOT OPEN AN ALKALINE BATTERY!!! It is messy and corrosive; carbon-zinc dry cells, while still messy to open up, aren't as bad as alkalines. Wear gloves and goggles, though. Basically, the outer casing metal can is zinc. There is also a carbon rod inside (save that for other experiments if you can), and the "dry" electrolyte substance, which is is the real messy part (it's black, crumbly, etc - do any disassembly outside - I got in trouble with my mother more than once taking apart batteries in my bedroom when I was a kid - lol).
So - there you have it - where and how and what on the parts.
As far as the electrolyte - it doesn't have to be a lemon. You could use water, with a bit of baking soda or salt (or both) dissolved in it; you could also use a potato; you could use cotton soaked in vinegar; you could use any number of things, actually - basically anything that can facilitate the galvanic corrosion. Different electrolytes will likely give you different voltage results - play around with it, and note your results!
Finally - and this is what I was going to get at earlier - you can make something better than just a simple lemon cell:
Take a piece of the copper pipe - with a reasonable diameter (1-2 inches maybe?) and length (maybe 4 inches long).
From the sprinkler section, get a couple cheap PVC pipe caps that will fit over the ends of the copper pipe; they don't have to be a snug fit, but should slide over the ends.
Get a hot-dipped galvanized bolt, along with a nut to fit.
Get some cotton twine or string.
Drill the centers of the end caps to allow the bolt to pass thru.
Slide one cap onto the bolt to the head of the bolt, then wind the twine around the bolt, the length of the pipe.
Keep adding layers of twine, until it is at least or a bit more than the inner diameter of the copper pipe.
Soak the twine in your electrolyte solution of choice.
Slide the copper pipe over the assembly, then slide the second cap over the end of the bolt.
Put the nut on, and tighten until you can't spin the copper pipe freely - if you put enough wraps of twine on the bolt, you may not have to tighten things much. Do not over-tighten, you don't want to break the caps.
There's your custom galvanic cell - the bolt forms one electrode, the copper pipe the other electrode.