Animated series has been done, I don't see another one covering the same details happening soon for a character like GL. I think a big budget TV series is the best way to go. I'm looking at what was done on Star Trek: Discovery and it looks pretty doggone cinematic for something that's supposed to be for TV. I have little doubt if you take the same budget and cut out the ships and special effects and sci-fi props you couldn't take that same budget and make some sweet construct action out of.
I think the real challenge for a live action show would be to find the drama. Outside of the action sequences, what IS a GL show? Is it a cop drama, with Lanterns paired up and investigating some sort of crime? Do they have a GL Vice division? Is it more of a political sci-fi exploration thing, like old school The Next Generation, where internal conflicts aren't the thing? Or is it the kind of cop drama where it's all about the varied interactions between the professionals and the way their personal lives and romantic lives and tragic pasts all get pulled into the overall professional struggle, whether it be being a cop, or a doctor, or a FBI trainee, or a Green Lantern?
I think that question is the most important, as it would strongly determine what the show is about.
Now what I don't think there's enough money for is to shoot on location in a city, and simulate constructs and battle damage within a city. I think that's too much for TV right now. Besides... all GL's best adventures are in space. Always have been.