Short spoiler: Still no truth, Luna lore/backstory, going into beach chapter
Long spoiler: With their close proximity, Naoto fights to keep lil' Naoto from reacting when suddenly, Luna asks about Naoto's plans for summer break. Naoto tells her that it hasn't been that long since he moved in, and it'll cost money to go back home so he'll be staying. Luna figured Naoto's mom would tell Naoto to come back home, but instead he was told to at least show up for New Years. Naoto then asks Luna's plans for summer, would she go back to her home.
Luna tells him that she won't. She haven't met with, hinted to be her parents, for years. Her dad's gone, presumably missing, since she was little, and she doesn't get along well with her mom. They haven't spoken much since her middle school years, which Naoto points out to be around the time Luna went to the countryside. This gives us age estimates of Luna being around 13~15 at the very least during the earliest of flashbacks.
Naoto said he didn't notice Luna's issues with her parents at all, but Luna said that's because of all the fun she's had spending time with Naoto all those summers ago, mentioning that it was the best, most special time of her life. Naoto tells her that it's too early for her to say that, as he declares that he'll update it all and that Luna should prepare for it.
Luna hugs Naoto, thanks him, and tells him she loves him. Days pass, and we reach August. Chapter ends with the whole gang (Luna, Naoto, Hiba, and Kawashina) in their swimwear at a beach.