I'm wondering whether "much of" can be replaced by "a lot of" to mean "a large proportion of" when the following noun is singular and countable. Many nouns have both countable and uncountable uses. For the present purpose, assume the nouns here are singular and countable.
Much of this cake was eaten by John.
A lot of this cake was eaten by John.
Much of this garment has been smeared.
A lot of this garment has been smeared.