Originally Posted by ISTFlyer

It is possible to upgrade them via miles or cash.

If you want to purchase a cash upgrade -> Log in through MMB on LH.com. If a cash upgrade is offered for your flight, it would appear on the reservation page.
If you want to upgrade with miles via Miles&More -> You could upgrade the flight in most of the paid Economy fare classes, however, Y and B would cost fewer miles.
If you want to upgrade with miles via another partner program -> You should be able to upgrade Y and B fare classes only, however, some FFP may have exceptions that you could upgrade cheaper fare buckets.