Unlike lambda calculus, OO is not a specific mathematical formalism but rather a methodology and ontology for organizing a program. Lambda calculus, defined by Alonzo Church, is a kind of 'arithmetic' of abstract function manipulation devoid of semantics. It has some strong theoretical footing as, in modern language, reflexive objects in a category.

> It's not clear to me why this makes Lisp not in the family of Lambda implementations.

To be clear, I started my comment by writing "if it is a realization, then it is one with [the following differences]." Lambda calculus was such a good idea that pretty much anything with function abstractions can be described by some variation of it. It's the dynamic scoping that causes the main issues here, though, and suggests lambda calculus was not a significant motivation in the definition of McCarthy's Lisp. Yet, he was still aware of it enough to call the abstraction operator "lambda."

>> Later, many of these ideas were backported to Lisp during the standardization of Common Lisp.

> Again this contributes to the notion that LISP/Schema/Lambda Calculus were "discovered", not that Lambda calculus has an explicit pedigree.

I don't see how that follows. Sussman was a math undergrad and PhD and was well aware of developments in logic, and he influenced Steele, who created the quite-influential Scheme and went on be one of the main people on the standardization committee for Common Lisp. This isn't even mentioning all the work people have done in PL research with typed lambda calculi (going back to corrections to Church's attempt to use lambda calculus as a foundation for mathematics), which has influenced the designs of many type systems in modern programming languages.