If an opponent targets Fiora with a spell while she is NOT mighty, and you react with Discipline to make her mighty (and thus grant her Deflect), does your opponent need to pay the Deflect cost?

No, your opponent does not need to pay the Deflect cost. Targeting is locked in when the spell is put on the chain, before Discipline resolves. At that moment, Fiora was not Mighty and did not have Deflect, so no cost was required. However, this differs from reflexive trigger spells like Falling Star or Icathian Rain, where targets are selected when the reflexive triggers resolve. If Fiora becomes Mighty while such a spell is on the chain, your opponent must pay Deflect for each reflexive trigger instance that targets her, since those targets are selected after the spell resolves.