I was looking through the forum and found some posts from 2014 and 2015 saying that there's not an easy way to export all your lists in Marketo at once. Is this still the case?
Or is there a way of getting an export showing that email@example.com is on List A, List B and List D for all the email addresses in the database?
There is no way to export all lists at once. However, what you can do is export the entire database with a smart list filter of "Person was created". You can create a custom field "Member of List A" that will be checked TRUE if the person is a member of that list. You can then bring this custom field into the smart list view:
Smart list criteria:
1 AND (2 OR 3)
Person was created
Member of List A: TRUE
Member of List B: TRUE
This ensures anyone who is a member of any of the lists is included in the smart list. You can then export the smart list members and the column will indicate which list they were in.