Qantas complimentary lounge access passes are only valid to access Qantas owned and operated lounges - not partner lounges - and are only valid in conjunction with and prior to boarding a QF flight with a QF flight number. Qantas operate in and out of Heathrow so they won’t have a lounge at Gatwick, but they do have a lounge in Hong Kong that’s pretty outstanding, however you won’t be able to use your pass there if you are flying with Cathay Pacific. Last I looked QF and Cathay don’t code-share on any flights into or out of Europe, so unless your Cathay Pacific flight has a QF flight number on it you won’t be able to use it there.
The only paid lounge I can think of in Hong Kong is the Plaza premium lounge. There’s two of them in terminal 1, and pricing generally starts at 50USD per person for entry - going higher in peak times and seasons, and they bill you by the time period you intend to stay i.e. one price for two hours, one price for five hours etc. Plaza Premium Lounges are global, however their only London locations are Heathrow so as far as I know in Gatwick there aren’t any paid lounges that will allow you to buy your way in as a one-off although I might well be wrong.