I have upgraded from 1.5 to 1.5.3: when I finished appear the message 'Lesson module needs upgrading' wiht 'Continue' button in Administrator user.
What the matter?
I think this is correct behavior. It is asking you to let it upgrade the Lesson modules database. After an upgrade you should go immediately to your admin page and let it run an update of the database. Just access http://yourdomain/moodle/admin and click ok on each page until it says it is done.