There is no arrival lounge at LCY. BA does have an arrival lounge in T5 at LHR but this is restricted to those on long haul flights.
If you check the lounge guide in the dashboard you will also be able to find out info about lounge access at your departure airport.
Also, many will argue that the benefits associated with travel in J are less so when flying in/out LCY as the aircraft is all 2-2 configured throughout and even offers complimentary refreshments in Y, unlike on routes to LHR/LGW.