Pokémon X and Y Walkthrough, Pokémon Move Sets: Lickilicky
(Please note that the recommendations below are largely made for in-game play. A Lickilicky in a competitive environment will likely make use of different moves to accommodate for smarter, more adaptive opponents. If you have a different moveset in mind for a Lickilicky, please share in the comments.)
Whomever designed Lickilicky and its predecessor Lickitung have some rather strange ideas about what constitutes a 'cool' design. Nevertheless, Lickilicky can be a very useful addition to your team if you need an HP sponge and don't want to use the regular crew. Apparently there's a lot of health packed into that tongue? Who knows.
Lickilicky starts off as the less-strange-but-still-pretty-weird Lickitung. To evolve Lickitung into Lickilicky you need only level it while it knows the move Rollout, which, naturally, can be learned at level 33. That said, you can breed a Lickitung with Rollout and transform it into Lickilicky as low as level two (which I recommend for making the most of its stats).
None. Immune to Ghost.
Lickilicky's stats are just about what you'd expect by looking at it. It boasts a fairly robust HP stat, backed up by high defensive scores. It's also pretty decent at Attack and, to a lesser extent, Special Attack, though both clock in at just a little above average. Lickilicky's biggest weakness is its Speed, which is fairly low... and, ultimately, unimportant to this bulky weirdo.
Own Tempo: This pokémon cannot be confused, either through an enemy attack or by using a move which may cause confusion, such as Thrash. Not bad overall, and more likely to come into use than the second ability.
Oblivious: This pokémon is immune to infatuation and taunting attacks (namely Taunt itself). Both of these are less likely to pop up in battle than confusion, but they're also usually more disruptive to your pokémon. Choose based on the opponents you expect to face.
Cloud Nine: Upon deployment, this ability negates the effects of weather (rain, bright sun, hail, etc.). Weather plays a crucial role in the movesets of many pokémon, particularly in online battles, and Cloud Nine can screw up a powerful strategy really quickly. Take that, Drought-bearing Charizards. This is a hidden ability.
Though Lickilicky can act as a regular combatant with its move pool and so-so offensive stats, it's better used as an extremely annoying tank. Start off with the king of irritating moves, Toxic. Follow up with Protect to allow your Lickilicky to stall while Toxic slowly does its work. Beyond that you'll want to add moves that will irritate or otherwise debilitate the enemy so they can't attack, such as Disable, Supersonic, Dig, and possibly Swagger, if you're feeling gutsy. Explosion is a possibility if you don't mind your Lickilicky being propelled out of the battle with its target; otherwise, Rest should be your final move. Couple Rest with a defensive stat spread and Leftovers and you'll have one hardy pokémon under your control.
EV / Super Training
Assuming you go for a standard Lickilicky walling build, you'll want to concentrate solely on absorbing hits. Pile EVs into HP to work up Lickilicky's health, then pump a bundle of points into Defense and, to a slightly lesser extent, Special Defense. (Fighting-type moves are your biggest concern, y'know.) If you really want Lickilicky to attack you can give it a normal-type move like Return and give it some EVs in Attack, but I personally prefer to boost survivability. Speed is unnecessary.
Catching a Lickilicky
To catch a Lickilicky you'll need to snag yourself a Lickitung first, and the easiest place to find one in Pokémon X and Y is in the cave sections of Victory Road. They're uncommon here, and a few battles should yield at least one Lickitung. These Lickitung are of a high level, so you'll have to visit Mrs. Remember in Dendemille City and hand over a Heart Scale to learn the requisite Rollout. (I still suggest breeding two Lickitung that know Rollout so you can acquire a Lickilicky at an extremely low level.)