Domain Lords react slowly to attacks on tiles if they are assigned to a production building.
They will often be the last responder to an attack, because the game sends one worker at a time.
If there's no way to make them act/respond like a military unit, an easy fix would be to give the 5% to all production in the tile they are in instead of having them assigned to a building, capping it at 5% so other domain lords wont turn it into 15%.
Video if img isn't illustrating it properly: https://mega.nz/file/YEsxkQpS#PWx7RgN3fb5Cc1rKUmByYg8CCtdnDWvhc5TI8z4Xbkw