He wasn't given a lecture about lambda calculus, he was giving a lecture about Y Combinators. While he gave a quick overview of lambda calculus (an overview wh

He wasn't given a lecture about lambda calculus, he was giving a lecture about Y Combinators. While he gave a quick overview of lambda calculus (an overview which I would describe as effective and _sufficient for the rest of the lecture_), that should not be confused with an attempt to give a lecture about lambda calculus. A more rigorous or 'correct' treatment of lambda calculus would not have improved his talk, it would have distracted from it..