Originally Posted by Polaritie
FFXIV likes to run automatically at Low, so its certainly possible for a program to change its priority.
The problem would be that both the matchmaking client and game client are launched by other programs, so I'm not sure what your options there are. Microsoft's resources are probably more useful here.
LolLauncher governs the priority of the rest of the process, change launcher to low, they're all low.
OP, this might not work, changing it to low causes the client to crash at the end of every game (for me anyways)