Lambert's daemon is going to be a chatty and irritable little marble polecat who will refuse a name from him and either come up with a name for herself eventually (aka when I come up with something suitably cheesy for her or if someone Lambert is close to ICly suggests something that catches her fancy).

She will generally be quarrelsome with Lambert, as she's most of the noble urges and affection that his cynicism usually keeps on a damper, meaning she'll keep prodding him to stop being an asshole, nobody's going to like us this way, as well as someone to drag Lambert to places he doesn't want to go. That said, she has as little a sense of personal space as he does, so she'll probably be inquisitive and nosy about other people's daemons and eager to play.

He's keeping a wary eye on that island -- the last thing he wants is soul-eating Spectres following them home, thanks -- and will probably be hitting up the locals to learn more about the area and that dimension-hopping technology, etc.