I lost plentiful of items before so I may be able to add something extra.
1. Left an iPod after a HKG-LHR flight. Reported it to guest service in GC then special service handed it back to me and I signed it.
2. Left a wallet at T5 arrivals lounge. I only realised it when one of the GAs called me. As I was at GC already waiting for another flight they kindly offered for someone to deliver it to me at the gate. What's special about this case is that I was asked if I would like to delays flight to MUC if they can not deliver it in time (they did at the end)
3. Left a brown bag in the EDI lounge. Realised it on the plane and reported but they couldn't find it at that point. Then called lost property and paid £7.50 to retrieve it days later after i returned.
My feeling is that it depends on your luck -- as long as it hasn't been handed over to loat property then you don't have to pay anything.