I think that the Green Lantern/New Gods: Godhead story arc would be a very good framework for the next Green Lantern film (Green Lanterns). They could loosely base the film on that story as follows:
The setting takes place in the Man of Steel universe after the death of Superman and the advent of Darkseid to Earth in Justice League: Part One. Hal Jordan is already an established hero, but has been summoned to Lead the Corps after the war of the lights (which will be explained in a future film). Kyle Raynor is the only white lantern who was able to pierce the source wall. This fact has been brought to the attention of Izaya, the High-father of the New Gods of Genesis. The rest of the story is about the history of the New Gods and High-father's quest to capture the rings of the emotional spectrum in an attempt to defeat Darkseid.
There are a couple of directors whom I think could produce a film like this. First off, Zack Snyder, who already has set down the vision for the DCEU is a definite candidate and so would be Peter Jackson. Geoff Johns and Snyder could create a treatment, but I would like to see Fran Walsh actually write the screenplay. My dream cast would be as follows:\
Ryan Gosling - Hal Jordan
Tyreese Gibson - John Stewart
Matt Damon - Guy Gardner
Alex Meraz - Kyle Raynor
Keanu Reeves - Simon Baz
Vanessa Hudgens - Jessica Cruiz
Mary Elizabeth Winstead - Carol Ferris
I won't name the members of the New Gods since I think they may already be cast from the Justice League film.