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Did you have a look at e.g. https://www.amazon.com/Theory-Objects-Monographs-Computer-Sc...?

Yes, that's one of the most prominent in a long line of attempts at creating formal models of OOP. And in the preface, you'll find:

> There is a well-established theory of functions, the λ-calculus, ... However, our theory of objects is self-contained; it is the first that does not require explicit reference to functions or procedures.

So that answers your question in the negative and proves my point: no, not every language is based on lambda calculus.

There are also different "schools of thought" for functional programming. That in itself is not a bad thing. The thread was about formal definitions; such are therefore available for those who need them.

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