“There are a lot of rumors”
“are” is acting on “lot” and not on “rumors”, since “of” makes “of rumors” an effective adjective on the word “lot”.
Since “lot” is a singular word (plural would be “lots”), “there is a lot of rumors” is appropriate, or “there are lots of rumors”, if you want to use “are”.
“There are a lot of rumors” is therefore incorrect.
This could all be solved by writing “there are MANY rumors”.