Fully agree to the first part, as far as the wake-up game in Injustice goes I personally split the cast in chars whose wake-ups I need to respect (good wake-up game) and those whose waku-ups I don't have to worry about (bad wake up game). And applying those two buckets, I would put GL in the later (view might differ depending on the options each opponent has to punish your wake-up game).
But at the end of the day thats just definitions I think we kind of agree on Lanterns wake-up game.
I generally hated it with Arrow because his knockdown and floaty jump doesn't allow him to kross up and going in is a risk because if GL blocks something then I'm forced to play defense against his 9 frame B1 and other options. Risk reward wise, Arrow doesn't do that much damage either.
Other characters kan deal with it better though.