How did Green Arrow find and access Prometheus' lair?

Yeah, in the "Rise and Fall" special. The Shade took him in to do the dirty deed. The Shade later creates a portal that gives Green Arrow access to Prometheus' other dimensional lair.

After Garrick was incapacitated by Prometheus , Shade was able to hold off the villain (as he is technically not a "hero", meaning Prometheus has no file on how to stop him), and ultimately ends up stopping Donna Troy from killing the supervillain after he has been beaten into submission. However, Shade later creates a portal that gives Green Arrow access to Prometheus' other dimensional lair, where the archer kills Prometheus in revenge for Star City, the dismemberment of his former protege Red Arrow, and the death of Red Arrow's daughter.

_{DC Database, Richard Swift (New Earth), History, Cry for Justice}