We know Lex Luthor hates superman because: 1. He took away his destiny of being humanity's savior and making people aspire to be like him/hero worship him 2. Natural xenophia to aliens and his belief that it makes human's too reliant on outsiders and weak 3. His belief of superman having malicious intent because he does not believe anyone could be that altruistic 4. Natural fear of superman having too much power and potentially going mental one day and destroying the world.
We know that AMAZO is a force to be reckon with and is capable of having the power to kill kryptonians easily.
We also know that it is entirely possible to transfer one's mind into a machine in the DC universe as evident by Metallo's origin story.
"John Corben was a professional con man until he was fatally injured in a car crash. The dying Corben was found by ProfessorEmmet Vale, a specialist in cybernetics, who was obsessed with the idea thatSupermanwas the spearhead of an alien invasion after he discovered the ship that brought the infant Kal-El to earth and mistranslated a message from his fatherJor-Elto his son. Vale took the helpless Corben to his lab and transplanted his brain into a cyborg body powered by Uranium, to which upon awakening the cyborg, instructed him to kill Superman."
So the question becomes if Luthor hates superman so much, why not just put your mind into an amazo like body that still physically resembles you and go kill him with your bare hands? Hell, tack on your kryptonite suit if you want for extra safety
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This could be you lex, if u were smart about it,