With regard to lex luthor being a hero; remember that the Brandon Routh Superman was supposed to be the Paragon of truth; and that for the Spectre's restart to work all the Paragons had to concentrate on the remaining scrap of the Book of Destiny.We don't know he made Lex a hero at all. That's merely what it seems to be at the moment. How that actually shakes out could be very different than first impressions. The fact that everyone thinks Lex his a hero could be due to something else that has nothing directly to do with Oliver.
My conjecture is that lex himself somehow managed the rewrite of himself as a hero /good guy. Like all the other Paragons; He still remember the original reality/multiverse too.
No matter how it plays out it does give the Supergirl writing staff an interesting character to used for future storylines.
They could even bring back Oliver/The Spectre. That character always works better if no one believes he exists, so that could be the explanation as to why he decided to appear as if he was actually dying to Barry and Sarah.