How do readers think T.Ray changed when August told Lily about how much he used to love her mother?
T.Ray himself does not change when August tells Lily about how much he used to love her mother - it's Lily who changes. She comes away from this conversation with a new understanding of her father and a much more sympathetic view. She realizes she is not the only one who has felt a hole in her heart due to her mother's absence; he, too, has felt the hole.
When he comes looking for her at the Boatwrights' home with plans to bring her back with him, Lily sees his pain - especially when he notices the pin she is wearing, which he gave to Deborah many years ago, and he begins to call Lily by her mother's name. He insists that this time, she's coming home with him. Both Lily and the reader see his desperation, feel his sense of loss from all those years ago, and realize the anger and abandonment he felt when Deborah left him, with no idea where she had gone to.
This new understanding of T. Ray does not excuse the way he treated Lily for all those years, but it does EXPLAIN his behavior. He became a hardened and bitter man after Deborah left him, and he took much of this out on Lily. As her father, he should have nurtured, supported, and loved her, and there is truly no excuse for his physical, verbal, and emotional abuse. Lily has every right to want a new life elsewhere, apart from her father. But, having called him "daddy" to break through to him when he mistakenly believes she is Deborah, we can assume they both walk away from the incident changed. Lily has a new sympathy for her father and an ability to forgive him for past wrongs; he, perhaps, can finally have some sense of closure on this part of his life and finally make a new and happier start.