Besides the fact that Hal helped show John the ropes in the comics, we already saw Hal’s origin told in the 2011 Green Lantern movie.
As far as the origin story aspect goes, since Green Lantern Corps reportedly stars Hal Jordan and John Stewart, I suspect the latter would be the one who will be the newbie.
As for the Lethal Weapon in space aspect, that’s a great tone for the movie.
The Green Lanterns are basically intergalactic beat cops, each assigned to protect a sector of the universe, so Hal and John could certainly have a Murtaugh and Riggs-like dynamic while they’re patrolling Sector 2814.