Battle Moveset

A Good Moveset for Lapras would have to be this:

Attacks:

Surf
Ice Beam
Thunderbolt
Confuse Ray

Items Attached:

LeftOvers

Preferred Nature:

Modest

Strategy Using Lapras

Lapras is one of those pokemon with high HP and decent defensive and offensive stats.
Lapras's movepool is varied and allows for quite a few movesets to be created. This moveset is simple to understand, there's one move to possibly gain an extra turn of attacking with the three other moves.
Surf and Ice beam gain a nice boost from STAB and cover many types that Lapras is weak against.
Thunderbolt is a nice filler move with the chance of paralysis that will help Lapras, as it has poor speed.
Like its been stated before, Confuse ray could allow Lapras to attack more frequently without being damaged in the process.

EV Corner:

Max out the EVs in Special Attack & Speed for Lapras with any remaining in HP

Strategy Against Lapras

Lapras' Defenses are a bit above average but it's Special is higher than it's Physical so a Physical Volley or a Steel/Electric Volley should work

Contest Moveset

A good Contest Moveset for Lapras would have to be this for the Beauty Contest best with Modest, Mild, Rash or Quiet Nature:

Attacks:

Hail
Blizzard
Confuse Ray
Body Slam

Items Attached:

Blue Scarf

Strategy Using Lapras

If you do the attacks in this following order you should have very few problems; 1st - Hail, 2nd - Blizzard, 3rd - Confuse ray, 4th - Body slam, 5th - Blizzard

Locations in Games

Ruby/Sapphire/Emerald Trade from FR/LG Colosseum Trade from FR/LG Fire Red/Leaf Green Silph Co., Icefall Cave

Animé Appearences

Lapras has had a fair few Animé Appearences. First appearance had Lapras under control of Santa out to look for one of his lost Jynx. After that, Ash & Misty found an injured one in the Orange Islands, after helping to rescue it from Team Rocket, Ash caught it and used it to travel across the Orange Islands and he used it in a few gym battles. After his victory Ash lets the Lapras go to be back with it's family to fulfil the promise of getting it back to it's family. A year or two after that, Ash met up with his Lapras in Johto. And after that a trainer on Cerise Island was able to control them easily Episode 065: Holiday Hi-Jynx! Episode 086: The Lost Lapras! Episode 087: Fit To Be Tide! Episode 088: Pikachu Re-Volts! Episode 089: The Crystal Onix! Episode 090: In The Pink! Episode 091: Shell Shock! Episode 092: Stage Fight! Episode 093: Bye, Bye Psyduck! Episode 094: The Joy Of Pokémon! Episode 095: Navel Maneuvers! Episode 096: Snack Attack! Episode 097: A Shipful Of Shivers! Episode 098: Meowth Rules! Episode 099: Tracey Gets Bugged! Episode 100: A Way Off, Day Off! Episode 105: Misty Meets Her Match! Episode 107: Charizard Chills! Episode 108: Pokémon Water War! Episode 109: Pokémon Food Fight! Episode 110: Pokémon Double Trouble! Episode 111: The Wacky Watcher! Episode 112: Stun Spore Detour! Episode 113: Hello Pumello! Episode 114: Enter The Dragonite! Episode 115: Viva Las Lapras! Episode 259: Lapras Of Luxury! Special 16: Pokémon Researcher Gary & The Revived Aerodactyl!