We would very much like to incorporate the course catalogue from the LMS into a page in the CMS. Is this possible, e.g. via a php include or similar? In fact, will it be possible in future to generally use pages from the LMS in the CMS?

Sorry, but it is not possible to include a page from the LMS into the CMS without developing a custom module for it.
Concerning your scenario, you can publish the course catalogue in the public area of the LMS and then link it from the CMS

OK, thanks.

The link to the public LMS is our current solution, which of course works fine. It means leaving the CMS, though, which is why incorporating the page would have been a "cleaner" solution.