A citizen of his Earth, Luthor's life presumably echoed that of his New Earth counterpart. However, his Earth's version of Superman, is apparently African-American, and as a result people were quicker to point out Luthor's inherent racism.
His activities are unknown. What is known is that five years after the creation of the Justice League, Lex Luthor was a "mad scientist" using robot warsuits to defend labs in abandoned buildings, while Superman was a key component in US President Calvin Ellis' plan to help fix the world.
As a result of a vision he had while on drugs, he built a bridge between universes, and when a monstrous version of Superman emerged from it, he helped his archnemesis defeat it before running from the Justice League.