On the Cathay Pacific lounge admittance page here is what they say
If you are travelling in different cabin classes within a single ticketed journey (e.g. from Singapore to Hong Kong in Business Class, and a connecting flight to Paris in Premium Economy), we will honour the highest class of travel (Business Class) for lounge entitlement* throughout your whole journey to make it a comfortable one. Please note that this only applies to flights operated by Cathay Pacific and Cathay Dragon.
So I believe you should be able to access the first class lounge in this instance as it is the highest class of travel within the same booking.