Enter Lumina's room at around 7:00 am and 10:00 am, 12:00 pm to 1:30 pm, or 8:00 pm to 10:00 pm. She will be glad to know you went out of your way to visit her. She was looking at an art book that Romana had given her and asks if you would like to talk for a while. You will be prompted to choose between two choices: "With pleasure" or "I'm busy. Maybe some other time."
For best results choose the former. she'll thank you and explain that the art book was about paintings that a friend of Romana's had made. She's always liked the paintings and feels a sort of warmth when looking at them. You can choose to respond with "What kind of paintings are they?" or "Are they paintings of fires?", either choice will be fine.
From here on, Lumina will be talking about the paintings. It doesn't matter what choices you make to her questions, you can't select anything that would be a negative response. Eventually, Lumina will thank you for listening to her.