It takes a lot of processing power to run this type of game on split screen. That's why you might experience lag when playing multiplayer mode on devices that are not high-end (Snapdragon 805 or higher, Exynos 7420 or higher).
To fix this problem, try closing all other apps while running the game. You can also reduce graphics by going to the device's settings, battery, power saving mode, and turning off ultra-power saving mode. If this doesn't help, try playing in single player mode instead, where there shouldn't be any lag issues.