When you’re playing as a Lich, one of the possible Lich Powers you can take will make your own animal companion, if you have one, count as undead (though the benefits of selecting that for a ranger/cavalier Lich Commander are debatable, since you get to select your own animal companion’s archetype, and so many of the Lich Powers are so good that it feels very bad to waste one on something an archetype can mostly accomplish).
However, this is not about the Commander’s theoretical pets’ potential zombification. This is about the undead Ciar. You see, Ciar already has his horse when he is raised as an undead and joins your party, but his horse has the basic archetype. This makes it awkward to heal the horse, since presumably a large part of a Lich commander’s party will be full of undead and negative-affinity characters. Furthermore, because you can only respec choices you made for your party members, and not the choices they made at levels before you met them, there is currently no way to give the horse negative energy healing on a permanent basis – you can only temporarily do so by casting a particular Lich mythic spell.
Please consider either allowing prospective Liches to choose the archetype of Ciar’s horse when raising him into your service, or forcing the archetype selection for Ciar’s horse to Deathtouched? It feels more in-theme not to have to devote daily spell slot effort to ensuring your dead cavalier minion has an appropriately dead horse to charge into battle on.