While they did show the negotiation with Margaret here and its outcome, the panels kinda skipped over a small but interesting detail regarding that deal from the novel: Theo mentioning Lightning's name isn't just him being truthful, it was actually a tip that Roland gave him as a trump card. Basically, if Margaret is proving to be difficult, Roland told Theo to mention Lightning being part of the expedition into the discussion to better persuade her, hence why as soon as Lightning's name came up Margaret changed her mind immediately.