Jason,
Let's start with requirement #1:
Each Course object
You have a Course object. Good.
maintains a list of the students on that course
You do have a list in the Course object. But it doesn't have a clear name. Your list implies it is a list of courses. But a course doesn't have a list of courses. It should have a list of students.
and the lecturer who has been assigned to teach that course.
You have a lecturer class. You still need an instance variable of that type in your Course class.