On a recent outbound I think I had about three hours, and as I have PP I used the lounge that is used by BA. On the Hermes (airport owners) website you can buy use of the lounge. Pleasant outdoor area that passed the time away before my LY flight around 10pm. On the return, having got the morning LY flight I hopped into a taxi, having left my luggage at the LL place in the departures and had a nice couple of hours at a restaurant on Mackenzie beach, organised the same taxi driver to pick me up and return to the airport for the BA flight.
There is also a Chabad House in Larnaca and a few kosher places if you keep kashrut.
All in all using BA reward flights means the return in CE is 50p each way and the LY flight around £140 retn.
I also paid 5Euro on the outbound LY flight for fast track security which really does help, no need upon return as I was in CE.
Hope this helps, I have done it twice now since the war began ( volunteering stints with Sar El )and will do it again in a couple of weeks.