LDAP login doesn't work after changing a users DN

A LDAP created user was transfered from one OU to another OU.
Now that user isn’t allowed to login in gitlab.

It seems to me that the login checks if the users current DN = DN saved at creation time. If not equal, no access.

How can I update a users DN in gitlab? (via API call?)

Have a look at http://doc.gitlab.com/ce/api/users.html#user-modification

There is a parameter extern_uid that you should be able to use