Viable?
I'm, a LC master, so I can honestly say that good ol' Super Fang/Quick Attack Rattata is very usable (For Ghosts, equip it with Pursuit. Good for the common switch too!) The last slot should be Swords Dance.
Chimchar is also good (Surprising, I know) for Fake Out, which gets a free hit in before sweeping with Flamethrower or Flame Wheel.
Carvhana works in a similar way to Sharpedo, who resides in NU: Many Pokemon can survive a STAB Crunch, but not a STAB Aqua Jet AFTER the STAB Crunch. A guaranteed 2HKO on 90% of the LC Metagame.
Finally, just like it's evolution, Bronzor is the star of LC. It's got mammoth Defenses (A cap of 22 for BOTH stats), a great support Movepool, and of course, carries Hypnosis for disabling and forcing switches.
These are regular members of my LC team, so you can't go wrong with them. =D
EDIT: Forgot to mention that Munchlax, Trapinch, and Porygon are the base of an incredible Trick Room Team.
Also, Surskit is a great choice (Again, I know, it sounds strange). It has access to Water Sport AND Mud Sport, so it can defend against LC's two-most dangerous types.
It also gets access to that good, makeshift water-type movepool. Ice Beam as well!
EDIT: Ohh, sorry Trach! The "Uber" Pokemon that are banned from LC are:
Scyther (WAAAAY too strong)
Yanma (Too fast)
Sneasel (Too fast and strong)
Meditite (Pure Power makes Meditite's STAB Hi Jump Kick way too powerful)
Misdreavus (It's a tad too balanced: Too much strength, too much bulk)
Murkrow (It hits like a truck)
Tangela (The stats are way too high for LC)
EDIT2: For more specification, only a Pokemon that evolves can be put into LC (So no slapping the level 5 Blizzard/Surf Lapras into your team xD), and it HAS to be in it's first form (No Jigglypuff, Clefairy, Pikachu, etc).
Also, a few more guidelines:
~Sleep Clause - Only one Pokemon can be put to sleep per team.
~Item Clause is negated. Your whole TEAM can old leftovers, if you want! However, Deepseatooth and Berry Juice are banned as hold items
(With Deepseatooth, Clamperl can reach a Special Attack cap of 28 at Level 5. Waaay too strong. Also, Berry Juice can heal every LC combatant to full HP, so it's banned as well.)
~Little Cup is pretty underground, and it doesn't get that attention, so even organizing a battle can be difficult. The only reliable LC community is on the CAP Server, located on Smogon.com's Shoody Battle Simulator.
