It seems John lilly had deep conversation with a large number of interesting figures so this one is certainly challenging.

Best guess at this point is that the person Lilly was conversing with was Oscar Ichazo who taught at the Arica school.

This drove Eliezer berserk because, as an avid proponent of rationality, the concepts and methods taught by Oscar have been topics which Eliezer has been working to debunk for decades. Lilly, having studied with Oscar, would likely have something of his teachings as the topic of discussion which Oscar would have to put up with.