inner join .... select top 1

Instead query like this:

SELECT TOP 1 * FROM Customers c (NOLOCK) WHERE Key = (mykey)

AND NOT EXISTS (SELECT 0 FROM Invoices i (NOLOCK) WHERE i.key = c.key AND i.Date > GETDATE() )

try to use this syntax:

select * from Customers inner join (select top 1 PK from ... order by ..) X on Customers.PK = X.PK

Usually it will behave better than select top 1 * from ...