I have edited the question for those nitpicking. It is a simple question.
The premise: "Many/a lot of" are multal degree quantifiers. "Not many/not a lot of" are their negatives. It follows that they correspond to some paucal degree quantifiers. If you think the premise is wrong, feel free to explain how.
The question (in 2 parts):
(1) Which paucal degree quantifiers do "not many/not a lot of" correspond to? That is, what can they be replaced with in
[Not many] things were done. [Not a lot of] work was done.
(2) When (in what context) does one use "not many/not a lot of" and when does one use paucal degree quantifiers?