I highly doubt this is going to happen. The game is in the making for 4 years now and it never seen even a single update that added to this whole JL vs. Lex, the threats being actual, idea. This part of the game, no matter how integral it seems at first, in my eyes became the forgotten and given up on part. When all the girls have their stories fleshed out there will be zero reason to retroactively start adding in further game mechanics. Thats just not how things work.
Its not unheard of, relatively common instead, that there are ideas and plans that while getting a little introduction into a game but never make it past that initial stage. I'd wager that this whole fight with the JL is one such thing. If they really reeeally wanted to do anything with or were serious to make it an actual struggle between them and Lex then wouldn't we have seen at least something in this past 4 years? I think so. Instead we have a completely pointless threat meter and several mention how the JL is going to be a thing. Content? Zero. I don't think they will ever make it into the game in any meaningful manner.