Martian Manhunter: He can fly, shoot lasers from his eyes, has super strength, and is invincible.

Which all makes sense. I can understand why he can't use freeze breath. Martians are vunerable to fire, so using superbreath he could put out the fire, thereby defeating his weakness.

That said I think the characters missed a really good chance, in that he is able to become intangible in the comics, etc. Why not use that and give him the same powers as Batman's sensor suit.

Green Lantern:
is able to fly, and is the only known character who can build sparkly, green LEGO objects.

Where to begin.....The most under-utilised character.
He should be able to at least shoot objects. personally I'd also give him the ability to put out fires (think Robin's Hazard suit but instead of water it would shoot out green goo). Basically Green Lantern should have every power, except maybe magnetic and laser. I can understand him not having laser ability since you use the laser to heat up gold objects. Which given that a Green Lantern's rings weakness is yellow, sort of, makes sense.

Cyborg
Cyborg is magnetic, able to activate machinery, and shoot lasers from his artificial eye.

This is only a minor thing. Just I'd change him from having lasers to sonic. The only reason I say that is that as far as I can recall he hasn't ever had an eye laser.