The cost reduction applies only to generic mana in the total cost of noncreature spells you cast.

To determine the total cost of a spell, start with the mana cost or alternative cost you're paying (such as a flashback cost), add any cost increases (such as kicker costs), then apply any cost reductions (such as that of Lyse Hext's second ability). The mana value of the spell is determined by only its mana cost, no matter what the total cost to cast that spell was.

Noncreature spells that were cast before Lyse Hext entered count. For example, if Lyse Hext enters on a turn where you've already cast two noncreature spells, she'll have double strike immediately.