A lot really depends on whether she knows about Clark or not. But if the story really revolves a cruel dictatorship and Superman having his own philosophy for how to deal with it, I think it'd be interesting to see Lois on the more cynical side at first and later be persuaded by his Superman-y ways. It would put her at odds with Clark while still having a good point of her own. Maybe it's an issue where neither of them is entirely "right", but her as a lone voice in media deciding to trust/support him when nobody else is willing to, I think that's a cool take.
Or maybe the other way around? She starts on his side and later realizes he's way too naive and his way won't do. Messier ending, less easy resolution.