Kevin could've seen the news reports of David Burton's claims that he died. They were in the background of a few different episodes earlier. His brain could've stored that away.

De-lurking here b/c I haven't seen this mentioned yet: I think it's clear Laurie decided to kill herself between the time she tussled with Nora and talked to Kevin. That's why the way she reacts to not having her lighter changes. She was finally ready to let everything go.