The answer is:
"I love thee with a love I seemed to lose
With my lost saints. I love thee with the breath",
the speaker refers to a lost love she once had for the saints and that now, it has returned.
Moreover:
"I love thee with the passion put to use
In my old griefs, and with my childhood’s faith",
the speaker compares a child's faith, which is pure and innocent, with her faith or religious life to emphasize how the love she feels now can change everything.