"above" vs. "over" vs. "in" the lake

Question

I'm writing a fantasy short story taking place on a platform that was built in a lake, but is tall enough to be above the surface. Since it's a short story, I don't really want to spend much time explaining it, but there's a decent chance I'll use that location again in future works, so I'd still like to give my readers a good idea of what it looks like. What would be a good way to do that in a single sentence?

As the title indicates, I've found three possibilities, but I'm not sure which would be best:

• "in the lake" - sounds like it's submerged, but could be what I'm looking for all the same
• "above the lake" - sounds like it was built on the shore, sort of like "overlooking the lake"(?), "looking over the lake"
• "over the lake" - sounds like it's floating over it

Any other ideas are welcome as well (as long as they are concise, of course), but I'd really like to just focus on those three, if possible

Answer 1

In Texas (many lakes) we would say "on the lake" ...as it carries you.

Answer 2

It extends above the lake surface.

The word extend suggests that the platform thing starts at or below the surface, but reaches a high point above the surface.

Collins English Dictionary:

If an object extends from a surface or place, it sticks out from it.
A shelf of land extended from the escarpment.

ODO:

1.4  [no object] Spread from a central point to cover a wider area.
• ‘the pipeline currently extends 1,200 miles from Santa Barbara’
1.5  [no object] Occupy a specified area or stretch to a specified point.
• ‘the mountains extend over the western end of the island’
• ‘a fault that may extend to a depth of 12 miles’

American Heritage Dictionary:

To be or become long, large, or comprehensive:   Influence that extended to other continents; table legs that extend by unscrewing.