In the movie Superman: Red Son when the US finds the Green Lantern alien,
why doesn't his ring fly off and find a replacement?
From what I understand: When a Green Lantern dies, the green power ring soars to the closest qualified alien.
A possible explanation is that Abin Sur was (artificially) comatose and not dead, therefor his ring would not seek a new owner.
A second explanation might be that in this reality, just like many other things that have changed surrounding Superman/Wonder Woman/Batman that this is no longer a thing.
This allowed Luthor to reverse engineer the rings making new ones that don't have the same user requirements as the original rings.
But it could also just be a plothole seeing it is never explained in the movie.