Yeah. Besides Luthor is too confident of himself, may be in his head thinking there's no way he could lose to someone who couldn't defeat a talking animal. And that will be his downfall.

I can especially imagine the argument around kryptonite.
Eggman: "You literally have the thing that weakens him! How have you not defeated him by now?"
Luthor: "Well, why don't you try giving your speedy little rodent problem green glowing rocks, see how that works!"
Eggman: "You fool! It will do the complete opposite of weaken him!"