I'd like to see the kingdom's also be able to use controlled monster lairs, even though they can't recruit monsters. My suggestion is that kingdom players make use of monster lairs be being able to use monster parts in researchable and designable objects.
For instance, if an empire controls a troll lair, they can build trolls. If a kingdom controls a troll lair, they can research and create troll blood amulets that can be used to equip champions/troops.
This change would make monster lairs a desirable resource for kingdom players other than to simply deny them to the empire player, without disrupting the human vs. fallen lore of the game.