Many and a lotof are not always interchangeable. Many can be used only with countable nouns (apples), whereas a lot of can be used with either countable nouns or uncountable nouns (money, milk, water, etc.).
Mother bought me many apples yesterday. Mother bought me a lot of
"A lot of" can also literally mean a lot of, where a lot is a grouping of products or services sold as a unit - e.g. "I went to an estate auction yesterday, where I bought a lot of furniture and two lots of paintings - one of landscapes and one of portraiture."