Consider this (extracted) sentence from the song "Yakkety Yak":
Let in the dog and put out the cat.
I would read this as
(you) Let in the dog, and (you) put out the cat.
where because both sides of the "and" have a subject, albeit implied, they are independent and should be conjoined by a comma.
Am I correct, or is the implied subject from the first side sufficient for both and makes the predicate contain the "and," thereby eliminating the need for the comma?