Haha yep, it's intentional. He has a sense of humor like that. Famously, he first presented his paper on the Paxos algorithm dressed like Indiana Jones with the fictional backstory of the algorithm being an archeological discovery of the ancient parliamentary systems of the Greek island of Paxos.
The paper is more of the same: https://www.microsoft.com/en-us/research/wp-content/uploads/... addmitadly, it's also fairly difficult to follow the random interspersed bits of Greek.
It feels almost like an intentional joke. Do you think that is the case? Or just even short segments were recorded on different days and Lamport like to wear all sorts of hats? That one where he's wearing a beanie and indoor sunglasses seems particularly intentional.
I've never met him, and the delivery of the lecture seems fairly dry and serious, so I can't tell :)