Hi alex,
I do not see this problem on my local moodle 2.5 test site. Using Moodle 2.5+ (Build: 20130606) and doing a backup/restore of a course with a Lesson with no password to a new course on the same server. Using mySql, Windows, PHP 5.3.
Have you tried a backup/restore of a course with a Lesson with no password to a new course on the same server, i.e. from your production to your production server?Ditto for a backup/restore of a course with a Lesson with no password to a new course on from your development to your development server?
Which system of database are you using on both servers?
Joseph
PS.- Since this does not concern the use of the Lesson activity as such I have taken the liberty to remove your post to the Lesson forum and suggest we continue discussion related to this problem on this Backup and restore forum.