The format you receive from queries is a "TableKey" type. It's not meant to be bound directly, but to be a convenient way for you to parse the queries and then manufacture the objects you need.
In your case, I'd recommend binding to the Bank object directly, not the key, like this:
var banks = from bank in App.Database.Query<Bank, int>()
this.Banks.ItemsSource = banks;
Then bind to "Name" and "NumberOfATMs" etc. without the LazyValue.Value prefix.
Your final save (each var bank in banks... Save(bank)) should then work fine, because save works against the actual entity, not the table key.