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Lightning obtains Eradia from rescuing a soul.

As the savior, you have a special life force—I call it Eradia. It's the power of God's light... It gives you your powers...

Hope Estheim explains Lightning the Eradia.

Eradia (気力, Kiryoku?, lit. Energy) is a term from Lightning Returns: Final Fantasy XIII. It serves as a source of power granted by Bhunivelze to the savior and is used by Hope Estheim to extend the lifespan of Nova Chrysalia by giving it to Yggdrasil which is placed in the Ark within the artificial Cocoon.

In-game, Eradia is gathered by releasing people's souls from their bodies, usually by awakening or resolving long-buried feelings. Sidequests and the five main quests award Lightning with Eradia, but Canvas of Prayers quests do not.