I've thought about this as well. There are servlets that handle import and export of sequences that could probably be called if you get your parameters/password/cookies right, but for the Moodle module the best arrangement would be to extend the integration in LAMS to support export and import methods (currently it does open author, open monitor, etc). This way get the good things an integration gives you, like automatic user/group creation if they've never accessed LAMS before, and server authentication.
On the Moodle side you'd simply call export/import on backup/restore respectively.
The current Moodle module can backup the reference to a LAMS lesson - i.e., when restored it'll point to the same LAMS lesson.
Posted by Jun-Dir Liew