1. He skipped stones over the lake.

2. He skipped stones on the lake.
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When the stones are jumpping on the surface of the water, what preposition can we use?

We would say "on the lake", but either is correct.

Thank you for your help.

What about 'across'?

3. He skipped stones across the lake.

That, too, is acceptable.

When the stones are jumping on the surface of the water, we typically use the preposition "across" or "over" to describe the action of skipping stones. Both sentences 1 and 2 can be used interchangeably in this context, although sentence 1 ("He skipped stones over the lake") may imply a longer distance or more exaggerated motion.