you are lucky, you can change to Miles & More!

if you want to hold some points on LX or one of the other programs i was told that you could charge the miles from your EZE trip to a new account, provided you take a new qualiflyer-account and it is also mentioned on the qualiflyer website:

Double Membership: I am interested in becoming a Member in more than just one of the new frequent flyer programmes. How do I proceed?

Until December 31, 2002

Yes, a Membership in several programmes is possible. However, please be aware that your mileage balance from the "Qualiflyer" programme cannot be split over several accounts. You will start as a new Member in any additional programme(s) you want to enroll to.
We will make sure that upon request you will be enrolled as a Member in either "Swiss Travel Club", "Navigator" or "Privilege".