"Is". Since the noun that "is" refers to ("a lot") is singular (we can tell it's singular by the use of "a"), we'd use the singular form of the verb, "is". "Are" is plural - for instance, you could say "There are a lot of things to do," because the object is the plural noun "things". However, in the sentence "There is a lot to do", one must use "is" because the object is the singular noun "a lot".

The choice of "a lot" or "lots" is completely irrelevant: There is a lot to do. There is a lot of work to do. There are a lot of jobs to do. There is lots to do. There is lots of work to do. There are lots of jobs to do.