A spaceship has crashed in the desert and the pilot is dying, his life seeping into the sands surrounding his vessel. He is a member of the Green Lantern Corps, intergalactic guardians of freedom and protectors of interplanetary justice. He orders his ring to seek out a replacement for him, a man of courage that knows no fear.
So the ring locates a man several miles away and starts leading the man towards the wreckage. Buffeted by the heat, the man makes his way across the sands, led by "voice" in his head. When he finally sees the twisted metal of the intergalactic ship, he is amazed, but still he moves forward looking deeper into the wreckage. He finally finds the body of the pilot, but Abin Sur is dead and no explanations are forthcoming from the weirdly costumed body of the extraterrestrial.
The man stands up, looking towards the horizon, wondering if anyone else has seen the remains of this ship. Before he can even consider his next step, the ring flies onto his hand and his mind is flooded with the knowledge of the Green Lantern Corps and that he is now a member of the Corps, guardian of sector 2814. No longer would he be a normal man. He will from now on be known as a Green Lantern, never again to be known as Jonah Hex!
I envision a Lantern even more bloodthirsty than Guy Gardner being unleashed upon the cosmos. Constructs based on the life of the Old West abound in the coldness of outer space. And perhaps, just perhaps, Jonah ends up encountering the original Terra-Man.
Feel free to dream and expound upon your thoughts. Personally I think it would be one helluva Elseworlds book.