Superman - useful
Batman - not so useful, Lanterns know he's smart so they take him out instantly
Flash - useful
WW - useful
MM - useful, but TP won't work
Aquaman - useless, TP won't work.
So now we're down to the JLA 4 vs. Lanterns.
Scenario 1:
I give the slight edge to the JLA. Superman and WW have shown the ability to break out of GL constructs before, and I've just never seen GLs be all that effective against serious bricks. Both teams will work well together.
Split 5/10
Scenario 2:
If Larfleeze has his entity, they stomp. Most recent Larfleeze doesn't though, so there's something of a fight. Lantern team will infight and argue, as they always do, and that's going to set them back some. Ultimately I think their numbers and firepower are going to take this.
Lanterns 9/10 - 10/10
__________________
"And then there was nothing. A once broken something now void.
And on the first day, Doom spoke... 'Be.'
And then there was life."
What's wrong with Batman? He was a member of the Big 7 JLA that went up against all sorts of major threats, a number of them worse than the Lanterns.
And remember the Hyperclan, another powerful team like the Lanterns... and who was the last JLA member left standing to save the day...
I see maybe Aquaman and MM running interference for Batman while Supes, WW, Flash are fighting. MM starts up the mindlink and Bats contributes the battle plan.