Licia's first ability reduces only generic mana in its cost. It can't reduce the cost below .

To determine the total cost of a spell, start with the mana cost or alternative cost you're paying, add any cost increases (such as the "commander tax"), then apply any cost reductions. The converted mana cost of the spell remains unchanged, no matter what the total cost to cast it was.

Licia's first ability checks how much life you've gained during the turn, not what your life total is compared to what it was when the turn began. For example, if you start the turn at 30 life, gain 6 life during the turn, then lose 10 life later that turn, Licia still costs less to cast.

If Licia's last ability is countered, it can't be activated again in the same turn.