Might need a bit more information than that...
What is the previous flight number, who operates it, and what class is it?
What is the subsequent flight number (departing HKG), who operates it, and what class is it?
Your post makes it seem like you are travelling intra-Asia on CX-coded CX in J, then on a CX-coded LX-operated to ZRH in F (I don't know any CX short/medium-haul routes with F).
Generally speaking, the official line is if all your flights are CX metal (the plane you board is operated by CX) then you'll get the highest lounge from your highest class CX flight, as long as it's within 24 hours AND on the same journey, as per the website
here (extract below):
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.