Unsurprisingly, The Justice Society will be set in the 1940s, more specifically, 1942 since that is where they will meet Damien Darhk, who, of course doesn’t know who they are. Screen Rant’s article also stated that Brandon Routh (Ray Palmer) had this to say about the JSA in season 2:
“So far what I know about the show, the season is Ray is pretty gung-ho about meeting the Justice Society of America and thinks they’re pretty cool, and they’ve got a well-oiled machine. And maybe the Legends can emulate certain aspects of that… This season opens up an opportunity to have a whole bunch of people back from the last season and from the other shows, as well. Because this season we’re not chasing Vandal Savage so we’re able to kind of do more of whatever we want. The whole world is open.
“Well we’re going back to the ’40s, for the JSA. That’s where we meet the JSA. And I think we’ll spend a fair bit of time there, in different countries within the 1940s. It’s the focus of the first couple episodes. And there’s a couple times we go way back. I actually don’t know how much I can say about where we go, I’ll have to ask Marc [Guggenheim[ that question. I mean, further back than we’ve gone… well… to one extent we go wayyyyy back, but for a portion of it we go… pretty far back.”
A big mouthful but yes they will be in the 1940s for quite a bit, which was alluded to in the season 2 trailer, as the Legends have to deal with Nazis, the classic bad guy to use. I find it to be very interesting that this is a substantial arc for the series. I said in an earlier article (which might have been changed) that I like seeing mini arcs for the grander scale of the TV show because I would like to see multiple missions from the Legends and see them grow as a team.
Source: Screen Rant