The Action Comics cover is incredible. Is that Lex on the Superman cover? I haven't read Year of the Villain #1 yet, didn't get around to it, but I did hear something happened to him.
"They can be a great people Kal-El, they wish to be. They only lack the light to show the way. For this reason above all, their capacity for good, I have sent them you. My only son." - Jor-El
Batman literally attempted to kill Superman in the last issue of JL, sided with the World Forger, and has now donned some future armor to battle the remaining JL. It's all a feint, but no one actually thinks Batman is EVIL now. Because it's obviously not where the story is going. The people who would hold it against Lois were not going to be convinced to like Lois by a different approach.
The box is probably symbolic, and I still lean toward Lex's offer as having something to do with wiping out Jor-El and his impact on their lives since his arrival.
"They can be a great people Kal-El, they wish to be. They only lack the light to show the way. For this reason above all, their capacity for good, I have sent them you. My only son." - Jor-El
Didio said it during a panel with Bendis and Frank Miller. There was a plan to keep Lois out of the books entirely for an extended period of time that Bendis shelved to have her come back. He's been setting up her solo book for Rucka since before he came on board. Rucka, Fraction, and Bendis have all said they more or less talked about his Superman plans and Rucka coming onto write Lois Lane and Fraction Jimmy Olsen while Bendis was hospitalized in 2017. There's various interviews from all three that touch on it.
I'm leaning toward Luthor offering her power to basically become his "queen" or whatever. The Lois/Luthor dating thing is back in continuity, so it's possible his obsession/infatuation of her is as well. It'd fit that now that he's Apex Lex he'd think she'd want him. He'd likely think her attraction to Superman was based on his being superhuman. So now he is as well, and can offer her the same power.
If the Lois/Superman affair thing is in play by that point, and it should be, it's possible he'd give her a "reset." Though it doesn't sound like his offers work like that. More along the lines of them becoming more powerful versions of themselves.
That sounds familiar, but could you refresh my memory as to when it was referenced that they used to date? Never really cared for the idea since it does lend a bit of credence to the "Lois digs power" thing, but I've always had to rationalize it as she was fooled for a short while that Lex was everything he claimed to be until she knew better.