What would happen in the story if a major character (i.e. Lyse) was tempered is unknown and unknowable; anything on the subject is idle speculation.

Tempering is, as I infer, the warping of the original being's soul into something favorable to the primal. As primals desire worshipers to maintain their aetherial existence and (in most cases) have them summoned to the material plane, that they would twist it into slavish devotion is unsurprising. (Side note: Ifrit is somewhat unique in just how obsessively devoted his tempered followers are - his "domain," so to speak, is domination, after all.) Without the ability to mess with souls, it's unlikely tempering can be undone.

That said - there is one instance of tempering being undone, Nael at the end of the Second Coil, so it's not impossible. There were unique circumstances surrounding Nael, though, so... who knows?