I assume yoy think it's just as bad to have dogs at the stable, and that the horses are absolutely terrified of dogs and can't ever get used to them? Dogs too are predators and naturally attack horses (in pack, but still predators).
Just because humans thinks lions are bigger, more excotic and dangerous than we'd thnk a wolf or dog, doesn't mean the horse thinks of it like that. It's no harder to get the horse used to a lion than to get it used to a dog. It's all about experiences.
Stat calm, let the horse get used to it and make the xperience with the other animal nice, the horse will accept it.
It's incredible what horses can learn to accept without being scared. Shouting crowds, fireworks etc not to mention having a human on it's back and steering.