Use the BA lounge where?
See this page at oneworld.com:
https://www.oneworld.com/members/fiji-airways
Basically, flying on FJ provides very limited lounge access. You can get access to lounges in Nadi or SIN but you need to be flying on a BA codeshare of certain FJ operated flights.
See also:
Oneworld Connect agreement
https://www.flyertalk.com/forum/30507350-post94.html
Fiji Airways - new BAEC partner incl. earn/burn and status benefits (start date TBC)