What do the dashed extended green lines on this PFD mean?
Those are radials off of the HME navaid, which is tuned in both Nav receivers. The two radials displayed correspond to the courses set in the two course select windows.

Putting a navaid's identifier into the FMC "FIX" page can also generate similar bearing lines, although there would be a green circle around the navaid in that case.

An ILS (also the departure runway in the flightplan) extended centerline shows as white, not green, and appears when that ILS (or any other) approach is active in the route, rather than when the frequency is tuned.