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You don’t need to create a new table for each user. You would do exactly what you said, have a single mailing list table and store each record with an associated user ID. Then, when a user wants to view their lists, you filter that table by user ID. Similarly, if a user wanted to modify a mailing list, you’d make sure that user has the same ID as the record they’re trying to modify.
Django already has a very powerful user authentication and permissions system. You should use it to ensure that only logged in users can access their records.
I suggest you take some time and carefully ready the Django documentation and follow the First Steps tutorials. They’ll give you a better understanding about how to set up your models and implement authentication.