I don't know much about this one except what is written on it, and that it is one of the few doubled dies I own (at least, I think it is). One other oddity on this one, it is neither medal nor coin alignment; the sides are at 90 degrees to each other.
It's a repunched letter so I don't think it's technically a doubled die since it's only one letter (well, more than one in this case if you look closely).
You may well be right. It's much more than just that letter that is doubled, however. Much of the word "LEWISTON' below the date shows at least some signs of doubling. The E in the larger word Lewiston is prominently doubled, and some others show less obvious signs. The letters in IDAHO, especially the H and O are doubled. Because all the letters are not exactly the same appearance, such as the N, repunching comes to mind. But because there are so many of them, I have concluded there is a second pressing with a slightly modified hub rather than individual repunched letters. Unlike mint coins, I don't know enough about the manufacturing process for these private tokens. Was there even a hub involved, or was each die individually punched with letters? If the latter, then of course this is just a case of repunched letters.
Take a look at both sides of this token. On the obverse you can see an obvious doubled "O" in "MO", but as you'll notice the "O" on the reverse does not. But that is not the only difference. Compare the position of each letter on either side and you'll quickly realize they're not the same die. If there were hubs involved, why not use the same hub twice to make each die? I also think it makes more sense to hand punch each die separately, since you're only make a few hundred tokens or less for a customer and never going to use the dies again. Here's a fun article. Scroll down the page and read "How Trade Tokens Were Made". https://tokenguy.tripod.com/tokentales/page10.htm Edit: I should note that some token dies were made from hubs, but most 1880's to 1930's trade tokens were not.
Die steel was expensive, so it makes sense that they would just punch one die instead of essentially making three - punch a master die, make a hub from that, hub a die - all for a small number of tokens. I like the N/N in the Lewiston one because it appears that they first used an N that was too small. "Oops, not that one."