Modelling Relationships in an E-R Diagram, Table or Foreign Key?
Your first option works best when there is the possibility that a lecture can have multiple tutors or when a tutor can teach multiple classes. Your second option works best when you can guarantee that a class will only ever have a single tutor at any one time (otherwise you would need multiple entries in your class table to accommodate extra tutors). The third one will only work if you can guarantee that a tutor will only ever teach one class (the opposite of the second scenario).

If you want/need maximum flexibility then go with option 1. However, you should choose the option that best suits your needs based on the descriptions of the types I have given above.

You can indeed over-normalize a database, and in some cases a de-normalized structure may suit the requirement better - but I don't think this is one of those times.

I hope this helps you.