There's not much backstory on Lady Comstock in the game proper. There's but one Voxophone that goes into any detail:
To those who loved me, I was the most generous of souls. There was no pain I would deny them. No betrayal I would not gladly give. And when I had scorched the hearts of all who loved me, the Prophet said, "There is nothing you can do for which I will not forgive you, for God has granted me sight, and through His eyes, even you are loved."
When I heard this, I interpret it as:
Lady Comstock was beautiful and had many suitors, ("those who loved me") and she was particularly abusive to them ("no pain I would deny them[,] no betrayal I would not gladly give"). It's possible she's also referring to her family, though.
This is still relatively vague, but:
In order for this to be something so terrible that it would require the level of forgiveness she references, I assume she must have been unfaithful towards her lovers. She seems willing to forgive quite a few serious transgressions the Prophet does, including mass murder.