The Cathay rules say:
If you're travelling on Cathay Pacific operated flights in different cabin classes within the same journey, you can enjoy lounge access if at least one sector of your journey is booked in First or Business class, and your connection is within 24 hours.
We will honour the highest class of travel for lounge entitlement throughout the same journey to ensure maximum comfort. In cases where the journey includes a stopover, lounge entitlement will be honoured based on individual sectors.
A "stopover" is well-defined as a break of more than 24 hours between flights. So the only grounds on which the person
cxwaterboy referred to being refused would be on the semantics of "within the same journey". What makes it a different journey? Different ticket? Different reservation? Midnight (or 6am as per OW rules) between the two flights?