What else can he possibly do in this story besides that? Childermass has come to all the same conclusions as Lambert has and it leaves him feeling useless. Worse, it makes him feel stupid for not turning away back when Lambert first did, but here they are now, going through the motions of a story neither expected. So, yes, he does comfort a specter of the witcher's younger self, in what little way he can.

He lets the boy snatch the handkerchief with no struggle, no additional 'you'd better return that laters', and instead turns to watch Lambert — the real Lambert — approach the doorway. He looks from him to the mother and father, then back again, quizzically though he can fathom from the expression Lambert wears, he isn't paying the magician much mind.