(Please note that the recommendations below are largely made for in-game play. A Lapras 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, toss it in the comments.)
Good ol' Lapras. An icy cold Loch Ness Monster that's as friendly as it looks, Lapras has long stood as one of the better pokémon to crawl out of the first generation. It's hard to kill, and has the raw power and move pool to bring down most opponents. You can't go wrong with a Lapras on your team.
Type: Water / Ice
Lapras does not evolve from or into any other pokémon. (For now. I predict a baby in the future.)
Electric, Fighting, Grass, Rock.
Statistically, Lapras does not stand out that much from other pokémon. Its Attack and Special Attack are pretty good; its Defense is okay; its Special Defense is better. Only its Speed suffers a bit, though it's potential serviceable if you feel like turning your Lapras into a speedster. Lapras' major strength its its enormous HP, which will allow it to survive even super effective attacks - which is good, given that Lapras has few resistances.
Water Absorb: If hit by a water-type attack, this pokémon will absorb the damage and convert it to HP. Not a bad ability by any means, but most enemies won't bother attempting to hit Lapras with a water-type move. Unless you can predict that an enemy will use a water-type move and quickly swap to Lapras, I recommend the second ability instead...
Shell Armor: This pokémon is immune to critical hits. Get this ability and very, very few attacks will be able to bring Lapras down in a single hit. I highly recommend Shell Armor.
Hydration: Any status ailments inflicted upon the pokémon will be cured by rainfall. Pair this with Rain Dance and you'll have a water-type masher that can't be paralyzed, poisoned, or put to sleep... the latter of which is fantastic if you equip your Lapras with Rest. This is a hidden ability.
There are two general directions you can take your Lapras. The first, given its move pool, is to turn it into a tank or sweeper. Lapras has access to a ton of hard-hitting moves, STAB and otherwise, and its durability allows Lapras to survive several hits while it creams the opposition. Use Surf and Ice Beam for your STAB attacks and a combination of Thunderbolt, Psychic, Hyper Beam, and possibly Dragon Pulse if you can breed it into your Lapras. Rain Dance is good for protecting Lapras if you have Hydration, and can make Thunder a viable and reliable threat.
The alternative is to turn your Lapras into more of a wall. Give it one or two STAB moves, then follow up with Toxic, Rest, and Rain Dance. Rain Dance will keep Lapras awake and alert whenever you need to Rest, while Toxic will slowly chew up the opposition. Your STAB move is handy if and when you run into a pokémon you think you can wipe out in one or two blasts; given its typing, I suggest Ice Beam so Lapras can become a competent dragon-type killer, something at which it has always excelled.
EV / Super Training
Lapras' naturally high HP count lends it to HP EV training, and for most builds you'll want to max this stat out. Past that you'll have to choose based on your direction. A sweeper Lapras should make use of Special Attack EVs, while walls will want to lean more towards Defense and Special Defense. If you want you can contribute a bit to Attack, but I find that the majority of Lapras' best moves rely more on Special Attack. Speed is last on the list; I generally don't recommend bothering.
Catching a Lapras
There are two ways to capture a Lapras in Pokémon X and Y. The first, easier method is simply to talk to the man at the entrance of Route 11 as you're leaving Shalour City. If you have space in your party he'll hand over a Lapras. Alternatively, you can find wild Lapras in Azure Bay, though they appear rarely.