Can the model with the "First Aid" ability use that skill on a model that had symbiotic armor but lost it due to getting hit?
Technically, Symbiont Armour is not lost, it goes inactive. When a unit with Symbiont Armour enters its inactive profile, it still has Symbiont Armour for the purposes of any rules that specify it. As Mahtamori pointed out, MediKits require a unit to be in the Unconscious State before you can use them, and an Unconscious unit with Symbiont Armour would always be in the inactive state.