it is normal to experience FPS Loss in BFV with your hardware in multiplayer matches since the load on the CPU and GPU is more than in single player specially on conquest and breakthrough game modes (i experience myself some drops and i am using i7 6700Hq and GTX 1060 laptop version, 16gb ram ). some of the FPS losses comes from the bugs in game like after a tank kill, some other comes from the heavy load on the hardware such as (V1 rocket explosion or artillery strikes). what is not normal is that the lag is continuing in the menus and lasting for several minutes my answer to that is to try and check the hardware temperature while playing your problem might be overheating of the hardware.
try and play on lowest settings using 32 players servers like TDM or squad conquest and check the results