As the other anon stated I think it was just that Alice had remembered that statement from whenever Lain stopped the rumors from happening. Lain no longer exists and so that vague memory comes to mind as she's struggling to remember something. Similar to whenever Lain changed time before. It shows Alice still somewhat remembers Lain because she was one of the few people who interacted with her directly. There's a similar scene with Taro when he sees her on his phone. They know they miss someone but they don't know who. That's probably the part of the series that makes me them most upset.