If you do not get on the flight you have a claim for denied boarding; nothing to do with OS/LH refusing to rebook at the earliest possible opportunity. If you get on the flight because LH successfully search for volunteers for VDB at the gate (which is very likely), you end up traveling as booked, i.e. nothing to claim for. If you get downgraded you have a claim for downgrade; LH will most likely make you an offer at the gate, but standard comp. according to EU reg. 261/04 is 75% refund of the fare for the downgraded segment (not the entire fare paid).

Do let us know how this turns out.