Hi Jane,
I am a chemist and I looked long and hard to find any description of the seasoning process with no luck. What follows should be considered my best guess and I don't claim any expertise, just some basic chemistry and some experience.
There are two questions I'll try to answer:
1. Why lye instead of the dishwasher? This is for the initial cleaning, not the cleaning you give your iron after you have seasoned it properly. That black junk that covers the beautiful cast iron comes from food - burned food! Burned food is a very complex mixture and not all of it come from polymerization. You can lump food into three major categories: Fat, protein and saccharides (starch, sugar and cellulose). All of them can be hydrolzed by lye (sodium hydroxide). 'Hydrolysis' comes from Latin and roughly translated means 'break with water'. Lye breaks chemical bonds (usually ones with oxygen or nitrogen) in these substances by adding water to a bond - one part gets one 'H' and the other part gets the 'OH' from H2O making two smaller molecules in the process. Lye is also a very strong agent for this and yet won't do anything to elemental iron. Hydrolysis products are usually more soluble in water too. A dishwasher basically removes food by softening it and emulsifying it with detergent. It doesn't really react chemically with the 'crud' on an old pan and that's why it probably won't work. Warming your lye bath certainly will help - an old chemist's rule of thumb is that reaction rates double with each ten degrees (centigrade) that you raise the temperature. Lye won't remove rust, but a vinegar bath will. Electrolysis will remove both crud and rust at the same time - that's why I'm anxious to try it.
2. What is the seasoning? This answer is out on a limb, so don't quote me as anything even close to an authority. The seasoning can't be just carbon because the typical heat used isn't enough to completely decompose the fat into carbon and carbon wouldn't stick to the iron (think charcoal!), in fact, really high heat would make carbon dioxide not carbon (this is what a self cleaning oven does).
Let's examine what happens when we season iron. Freshly cleaned and naked iron is very reactive, as we all know too well, and will rust if you look sideways at it. Fat, left at room temerature, turns rancid after a while. When you put iron and fat, together with some heat, magic happens! The iron won't rust, the fat won't turn rancid and the two are not easily separated. This tells me that the fat reacts directly with the iron, forming chemical bonds that are relatively strong and resistant. I'm sure there is some polymerization, but I think the iron/fat bonds are what do the work in our cookware. The fact that repeated use improves the seasoning tells me that more of the surface iron atoms react with more fat molecules - I don't think it would improve if it was just a polymerization reaction, in fact I think it would get worse with time.
I hope this helps and isn't too long or too technical, but it's not a simple issue.
By the way, I don't use bacon fat for initial seasoning because of the smoky chemicals and the salt - these might react with the iron adversely. though nobody seems to complain about it. I use Crisco, but any pure rendered hard fat (lard, suet, etc.) should work fine.
The first thing I usually cook in freshly seasoned iron is scrambled eggs with butter (well, maybe not in a waffle iron!). If it sticks, I didn't do a good job seasoning, If the eggs get a greyish color, I didn't clean it well enough (the dogs don't seem to mind).
Here's how I clean my seasoned iron: while still warm, I rinse with hot water & wipe out the bigger bits, then I dry it and use a little paste of kosher salt and neutral veg oil like canola (not olive or other strong flavored oil) then use a paper towel & the paste to scour the pan clean. I give it another shot of hot water, dry it & hang it back up. It seems everyone has their own little ritual.
Cheers,
Jim Maloney