The answer's changed a bit. Everything PrimalKyogre said is still true, but there's a few Pokemon that have risen to prominence (or at least are fairly threatening) in more recent times.
Abra
Incredibly frail, but incredibly powerful. Sporting one of the largest Special Attack stats in the game (tied with Solosis, who no one uses) and a large Speed stat, it can rip through a lot of foes. Focus Sash allows it to counter an opponent that would ordinarily OHKO it (Pawniard, Grookey, etc.) and continue to sweep. It's very susceptible to common moves, however, like U-turn, Knock Off and Sucker Punch.
Archen
It has the single largest Attack stat in LC, which makes it an instant threat. It has Dual Wingbeat and Acrobatics for reliable STAB, Knock Off for Eviolite abusers, Head Smash as a ridiculously powerful STAB move, and can Defog to remove crippling hazards. It's crippled by Defeatist and to an extent its Speed tier, however.
Dewpider
Dewpider is a prime lead. It can utilize Sticky Web and Icy Wind for speed control, and it's not a bad attacker either. It has an excellent Ability and Giga Drain, meaning it can stay in battle for a good while.
Foongus
Foongus is extremely annoying. Spore allows it to cripple an opponent and bring in a teammate to set up, plus it can easily recover health thanks to Synthesis and Regenerator. Its bulk is accentuated by the Eviolite, meaning without Knock Off, it'll be very difficult to take out.
Grookey
Grassy Surge Grookey can be terrifying. It can set up Swords Dance, making it into a very potent threat. With automatic priority Grassy Glide, it can break through a lot of walls, especially when coupled with Knock Off, which allows it to remove Eviolites and other annoying items. Drain Punch prevents it from being walled by Magnemite, Ferroseed, and other Steel types. Using an item like Focus Sash or Grassy Seed in conjunction with Acrobatics gives it a massively powered Flying coverage option as well. Wood Hammer can also be used for brute force, and U-turn for pivoting. Overall, Grookey is a definite menace in LC at the moment.
Magnemite
A more stall-based Berry Juice + Sturdy strategy. With Recycle and Endure, plus being immune to Toxic, it can stall out an opponent, and pivot with Volt Switch. It's crippled by Knock Off, however, so be wary.
Mareanie
One of the best walls. Eviolite, Recover and Regenerator make it nigh unbeatable without the right Pokemon, and it can spread burns and toxic poison with Scald and Toxic/Toxic Spikes respectively. It's a very annoying Pokemon to fight, and it has the potential of crippling a valuable teammate.
Onix
The most popular strategy is Dragon Dance + Sturdy + Berry Juice, with it being occasionally used to set up Stealth Rock. Sturdy activates Berry Juice and brings it to full health, essentially giving Onix a free Dragon Dance. Then, it can proceed to sweep entire teams if you're not careful.
Pawniard
With a gargantuan Attack stat, Knock Off, Swords Dance, Sucker Punch, Brick Break and Iron Head, it's a fearsome physical attacker. Any good Fighting type can KO it, but it'll be difficult if you let it set up too much.
There are other threats, but these are some of the more dangerous ones. If you'd like me to elaborate on any, I can, and if you'd like me to add any other Pokemon to the list, I likely will.
Hope I helped!
