There is a new 24 hours food court near Gate 11 now in the air-side/secure area at Terminal one!
It basically has a 24 hours McDonald/McCafe, along with a Hong Kong style cafe/diner "Men Wah Bing Teng" in the lower level (Level 6). There is a pop up coffee shop but that is only opened between 6am and 11pm.

The Food court next to the immigration will also remain open - Putien (a Chinese food fast food joint) and Gordon Ramsay are the only two eateries that open 24 hours.

There is a Plaza Premium Lounge that is opened overnight near the end of the concourse at Terminal One. I believe some airlines like Thai Airways will host their crews there during the short turnaround between the late night arrivals and morning departures. It is a paid lounge though.

The last CX flight of the day is CX 844 that departs at 2am local (plus and minus depends on the season but around 2am), and the only CX lounge that will remain open after midnight is the Wing First/Business Class. The Pier First/Business and the Deck will close at 12:30am. All lounges once again reopen at 5:30am.

Once again your connection flight was for the next day and there is just no way that Cathay Pacific lounges will let you in. Unfortunately, Hong Kong Airport has no transit hotel airside (like Changi or Incheon airport). You will just have to walk around a quiet airport for the night. The CX lounge will reopen at 5:30am and you will be welcome to use it then.

I am also curious on your friend's experience.