I'm not 100% certain, but I think "lots" is the plural form of "a lot". So whether you use "lots" or "a lot" depends on whether the word it is modifying is plural or singular.
In "there is a lot of noise outside", noise is singular so "a lot" must be singular.
In "there are lots of noises outside", noises is plural so "a lot" becomes "lots" (its plural form).
I'm not sure if that answers your question, but I hope that helps.