On other airlines you can take a wedding dress with you (even in Y) but it must be within your carry-on limit - size and weight - and they certainly wont hang it in a closet.

E.g. VS - http://virginatlantic.custhelp.com/a...ress/related/1


And yes you can pay for a seperate seat for it - you need to phone LH to book this though. AFAIR you only pay the base fare (no taxes) for the extra seat but it does not attract a baggage allowance in its own right. The box of whatever it is being carried in would need to fit into the seat and have the seat belt around it too.