Called MPC HK, the agent's first response was no you do not, regardless of connection length. The "reason" she offered was that, for your onward J flight, because CX already has a J lounge that you can access, therefore no special arrangements would be made for you to access the F lounge.
I mentioned this seemed to be in conflict with at least the OW rules, she offered to call the airport lounge staff to confirm, and the reply was yes, you can use the F lounge if coming off an F flight
for a transit to a J.
I specifically asked if anything changes if the onward flight, while within 24 hours so that it qualifies as a transit, was on the following day, she said this does not matter as you are still transiting. You can access the F lounge at any point during your transit so long as the lounge is open. But if it is over 24 hours, it is not a transit, and you will not have this access.
So this is good news for you
