If there's such a website that does just that, it would be tricky since there are some addresses in which the coins hasn't moved for years only to know they're active and being used as cold wallets. That would also be a unique idea since we'll have some form of basis as to how much really was lost and how much bitcoins are left circulating around the network. It would be pretty hard to implement though, and I don't think some parties or devs would do it just for the fun of it.
I think it would just be a submittal thing, like User A would say I lost 6mbtc, public address was x.
Table would have public address and the exact amount on blockchain, if there is any movement of coins this row would be deleted off the table.
It's pretty hard for somebody to prove he is the owner of a lost wallet, as the only to way would be for him to sign a message...which he can't.
So it will be basically down to claims of, which can never be fully verified.
I thought I've had the link in my bookmarks but I can't find now, there was a website that was monitoring addresses with a balance that have never moved their coins. With a few tweaks it can show coins that have not moved since x days and combined with wallet explorer you can greatly reduce the amount of coins that can be "considered" lost or at least sleeping till the owner finds his keys.
