Is "a lot" only used with countable or plural words?

Is it grammatically correct to say: "A lot of food is eaten" or "There is a lot of milk"?

Isn't "a lot" only used for plural and countable nouns?

Should the sentences be: "A lot of food are eaten" and "There are a lot of milk"? Or should they be: "Much food is eaten" or "There is much milk"?