a lot=very much 是副词短语，修饰动词

吃的多 睡大觉 多谢

eat a lot

sleep a lot

thanks a lot

a lot of=lots of是形容词短语，修饰名词

许多学生 许多朋友 许多钱 许多人

a lot of students(可数名词)

a lot of money (不可数名词)

a lot of friends (可数名词)

a lot of people (不可数名词)