"On the lake," because a boat floats on top of the water. If you said "in," then the boat would be thought to be submerged in the water.

I went to lake for boating is correct.

The preposition in is usually used with the notion of "inside": "He is in the car" = inside the car Already the preposition on is used with the notion of "upon" of something or surface: "The cat is on the table" The correct answer is "I went boating on the lake."

On