I'd be careful about taking the reservation agents word for anything like that. They're trying to get you off the phone so they can take a booking!

Since you don't have any right to lounge access (by CoS on your next outbound flight or OW status) for the F=>Y transfer in HKG, the only thing you can do is ask the lounge agents. If they are nice, they may make an exemption but don't expect to get lounge access. If the Wing rejects you, try the Pier or v-v.