Well, I figured it out. It is possible to start Livesync with a teamwork file, if you start a fresh Lumion file. You can't update an already existing Lumion file that you've imported a .dae file into. But I also found a way around it - I changed the name of the file on TW BIM server, started a Livesync to a new, empty Lumion file, and then merged this new file into the old Lumion scene, so it kept all the Lumion things in place (items places, views and settings saved), but replaced the old .dae file with the livesync model from the new file.
Seems a bit stupid to go through this loop, but it solved my problem. Did not want to create a new Lumion scene at the end stage of the project, but adding Livesync makes workflow so much better, so.. the loop was worth it.