These are his rational thoughts. He didn't know why Iris said what she said. Did she say that out of her overwhelming emotions, or is it her rationale?
If it is her rational decision, does she still thinks she needs more punishment?
"Let's cross that bridge together then. It's a promise."
For Arthur, Talia's decision seemed as over-compensation. He personally won't let her do anything too much. But if that is her decision and she insists, he won't let her face it alone. He'd stand by her side and help her get through this.
Arthur's gentle voice that gave her another promise, made Talia freeze for a moment. He doesn't think twice before he gives his promises, right? How valuable are his promises then?
But then why does this promise give me so much courage?
"I'll hold you to that," she smiled. Suddenly she felt like she could face anything that awaits her when she faces Lord Lockhart.
