Certain archetypes we haven't seen yet;
An aquatic character. Tellus was aquatic, but didn't have any aquatic-based powers, like super-swimming or controlling sea-life or, more usefully, throwing tidal waves at people.
A 'summoner' able to create adversaries. Triad is the closest, being able to create a pair of allies of equal strength, but there aren't any Air Controllers able to whip up mini-tornadoes to chase people around, or Technos able to gesture and make surrounding machinery turn into temporary robot servants or a Living Hive able to expel swarms of venomous alien wasps to bedevil it's foes. Life Lass is the best example of such a character. Quislet doesn't count, since he effectively *becomes* the new adversary, making him more of an exotic shapeshifter.
The 'hard whatever' object creator. Green Lantern with his power ring, Mera with her hard water, Lightmaster with his 'solid light constructs,' Songbird with her solid sound energy constructs. Someone able to make walls and grappling hands and shackles to hold the prisoners and big spinning fans to blow away incoming toxic fumes...
Definitely a Healer. It doesn't have to be an OMG healer who'd wreck the dramatic potential of the characters being at risk of harm, it could just be someone, like Raven, able to soothe injury, sustain the wounded and, at great risk to themselves, repair damage. Also better if, like Raven, or the New X-Man Elixir, said Healer isn't completely useless in a fight...
Fall-Down Boy. Someone able to, like the Spider-Man villain Slyde, New Universe character Friction, or the Savage Land Mutate Vertigo, make people fall down, whether through slippery secretions, control of friction coefficients or induction of vertigo / nausea. I've always loved that sort of power. [Point and laugh, as bad-guys fall all over themselves.] With friction control, Fall-Down Boy can also be Can't-Get-Up Lad, making the ground infinitely 'sticky' so that his fallen targets are effectively pinned.
Sonic powers. Tyroc doesn't count, because he just had magic powers that did random crazy crap when he opened his mouth, much like Chemical King and his power to wave his hands and make the next panel fill up with some dubious technobabble rationalization for whatever random thing just happened.
Speedster. A DC staple, that the Legion didn't get around to adding until XS, and then duplicated by giving Kid Quantum II similarly effective powers.
Turns to Energy Lad. Wildfire had this, in concept, but didn't actually walk the walk, spending most of his time in a containment suit. Something else else like Marvel's Captain Marvel II / Photon / Pulsar, or Lazon, or the Super-friend Black Vulcan, able to turn into a bolt of energy and smash into people.
The Scrapper. Like Karate Kid, this ones a close-in fighter, but uses some sort of schtick, like a quarterstaff of living force, or a silk-steel whip, or the magical blade of their ancestors, or just a really crappy attitude and meter-long claws of unbreakium.
Vampire. Able to steal powers from another. Or maybe she steals life-energy, and can use it to empower herself, or even to heal her allies?
The Destroyer. Many Legionnaires can unleash desstructive forces, but this character would be just that, able to disintegrate objects at range. Maybe he uses acid, maybe he unbinds nuclear forces, maybe he just makes things go away by disbelieving them intently. In any event, he's Saturn Girls polar opposite, hell on robots, up a creek against monsters who are not reliant on weapons that he could make vanish.
Huh, between the power-thief, the clawed psycho and turns-to-energy-lad, I think the League of Super-Assassins covers quite a bit of missing ground.