As a general rule,
almost anything anyone ever succeeded in doing in the DCU,
@King crimson is willing to let us do if we figure out how to make it in-character plausible given the resources and options at our disposal.
Given that we're playing Lex Luthor, our resources are almost unlimited for purposes of "can you mad-science up _______." We even had a guy on payroll, Dr. Ivo, who was trying to make an immortal and absurdly powerful robot body, and while the DC of his actions eventually became so high that the project fell apart, we didn't run out of
money, and in hindsight we could probably have accomplished (or could still accomplish) the project even with him dead.
So if we want to become AMAZO or have an AMAZO body, that's an option. Less ambitious forms of immortality would probably be easier to achieve.
The main limit on our options is that Lex has to know in-character that a thing can even be done at all. For instance, right now we have no option for "hide kryptonite in Clark Kent's desk just to fuck with him" because in-character, Lex doesn't know that Superman is secretly Clark Kent, and Lex would have no reason to do that to a random reporter at the Daily Planet that he's only vaguely aware exists.
Be careful; this is a comic-book setting. Having intelligent AI could make some forms of cyber-attack harder but others
easier, and we would have to make sure our AI stayed loyal.