much and a lot mean the same thing, but we use 'much' with non-count nouns and 'a lot' with count nouns: I don't have much money, time, water I don't have a lot of pencils, books, coins

They are synonyms: 'much' means 'a lot of' (when used with non-count nouns), and there's no reason why they shouldn't be freely interchangeable, at least grammatically speaking. Generally, though, it's often just a matter of style, 'much' being perceived as the more elegant of the two, especially in negative clauses.

Best Answer's answer is perfect...

much = a lot of