Instructions
Equip as many Super Repels as you can carry. Use these as soon as you enter the cave and again whenever one loses its effect. This will keep away common, weak Pokemon and ensure that, if you encounter something, it will almost surely be a Lapras.
Surf up and down in one of the many freezing cold pools using one of your Water Type Pokemon. You are far more likely to find a Lapras surfing in the open water than you are fishing from the shore.
Use an Ultra Ball when you encounter Lapras. A Pokeball will fail every time, and a Great Ball is also unlikely to get the job done.