Had this with mine, I did replace the small cable inside which made it better but still opens the door using the left end of the lift handle, I think its down to wear on the plastic nib on the internals that activate the lock that causes this. Its a door card off job to get the unit out and poking the locking slide across through the access hole on the edge of the door. How to on Youtube here
Another video for taking the lock unut out here
Parts diagram on Realoem, here is mine for the 2.5 E85
BMW parts Z4 E85 Z4 2.5i Locking system, door, front
www.realoem.com
View: https://www.youtube.com/watch?v=zByNn9DYbzI&t=256s
View: https://www.youtube.com/watch?v=yZ9iWny9iTg