Yes, but punctuate it like this:
On the left were the sinks; on the right, the stalls.
The comma I have inserted is a gapping comma to show that words have been omitted instead of repeated - in this case, the word "were" has been omitted.
I've also replaced your comma with a semicolon. This is to fix a comma splice, also called a comma fault - when you join two independent clauses with a comma and no conjunction. Your second example has a conjunction ("and"), so in that example, you could just insert the gapping comma in place of "was".
Some comments have suggested that the semicolon is unnecessary, and in most cases I would agree that it is. As a semicolon is read as a pause in the same way a comma is, most modern English writers just use the comma. However, when the gapping comma is inserted, the two commas could be confusing to a reader as they may not discern as quickly why the second comma is there. Changing it to a semicolon avoids that confusion and makes it obvious that there is a gapping comma. I'm not being dogmatic about this latter point and you can take or leave my advice.