This is happening way to much recently and its more common in Competitive mode than Control in any other playlist. How can i shoot someone the shot doesn't register, they then kill me, then my shot registers on the person who is lagging. And before anyone comments about my ISP or it being on my end, i have no issues with my ISP or any other games, When my clan plays comp as a fireteam of 3 and all 3 of us notice 1 person on the other team lagging, or deaths registering delayed there is clearly an issue in the game/servers which needs to be looked at as it ruins the pvp experience for other players, and can sometimes be game changers especially in comp.
Report them and move on. Nothing more you can do.