I saw someone on Twitter the other day point out that, in fact, with these conversational AI -- and LaMDA was trained quite specifically, as Google noted in its original blog posts about LaMDA, on textual conversational dialogue -- the bots' training corpora quite likely included tons of novels and tons of sci-fi that has, as you point out, for decades featured AIs that become sentient.

I wouldn't be surprised if it's channeling some of that training ...