on/at the other side

[M. Shelley]

Hi.

- The houses are across the lake.
- The houses are over the lake.
- The houses are on/at the other side of the lake.

I think all the sentences mean the same. But, in the third sentence which preposition is the correct one?

 

[SPQR]

- The houses are across the lake.
- The houses are over the lake.
- The houses are on the other side of the lake.

 

[obz]

- The houses are across the lake.
- The houses are over the lake. (están flotando en el aire sobre el lago...)
- The houses are on/at the other side of the lake.