I have a question about this. I made the sentences below myself:I own a house on the lake. This sentence means not that the house is on a platform in the middle of the lake, but that the house overlooks it or is adjacent to it.
'A house on the lake' means the house overlooks it or is adjacent to it (from post 3). The house doesn't need to extend over the lake, butSentence #1 suggests that the boardwalk extends over the surface of the lake (which is not uncommon), and that you will walk on the boardwalk over the surface of the lake.
The full sentence was " I am going to take a walk on the newly built boardwalk on the lake." If the boardwalk did not extend over the lake, it would be much more natural to say "... the newly built boardwalk by the lake", or "... along the lake", or "... next to the lake." I do not find "... on the lake" to be very natural generally (to describe a boardwalk, that is; I have no problem with using it for a house), and so if it were used I would think it had the meaning of going over the water.Not to me.