A few years ago, who'd have imagined we'd ever see the Elongated Man on TV, or Grodd fighting King Shark, or a battle between a giant demon and a giant Beebo? The Arrowverse FX team has had years of experience pushing the boundaries of TV visual effects.
They also have a bunch of accumulated digital assets that would be easy enough to re-skin as translucent green ring constructs. You want GL to construct a gorilla, they can re-skin their digital Grodd or Solovar. You want a T. rex, they've got one in their library. Other animal constructs could be repurposed from the FX for Vixen's ashe animal spirits. Same if he creates a submarine, a jet plane, a missile, or any of the hundreds of other objects they've created digitally over the years. Or consider the battle between Killer Frost and Icicle last season on The Flash, where they were creating ice ramps all over the city. If they can do that, they can do ring forcefields and barriers the same way. So doing the ring constructs would be relatively easy.
The challenge would be depicting alien worlds and species, but Supergirl has gotten by with mostly humanoid aliens, and for that matter so has Agents of SHIELD over on the other side of the fence. Maybe you could have a show that focused on humanoid Lanterns like Katma Tui or Boodikka, with only occasional appearances by CGI aliens like Tomar-Re and Kilowog. Or, heck, I could see Kilowog being pulled off with prosthetics, with some modifications to his design.