OwnValues et al are the transformation rules used to evaluate expressions. A Lisp program must also maintain transformation rules somewhere in the execution context. So you and your friend seem to be largely in agreement.

As for lambda calculus, it might be more accurate to say that it serves as inspiration for both Lisp and WL. But maybe that equates to quintessence--I won't quibble.

But these comments approach the question by looking at the form of WL and its model of execution. An alternate perspective would be a sort of teleological one, and from this perspective I think Stephen Wolfram's own words might be the best answer: https://writings.stephenwolfram.com/2019/05/what-weve-built-is-a-computational-language-and-thats-very-important/