It's funny you say that because I'd say FP has a much more well defined mathematical foundation compared to OOP. In fact, before it became as dominant as it is today, it was often criticized as being too scholarly and theoretical. It's built mostly on the foundations of Lambda Calculus (and maybe some Type Theory).
I don't think OOP ever had nearly as strong of a mathematical/scholarly foundation as FP has
In that sense, every programming language (as well as lambda calculus) is based on Java, since Java is a universal model of computation. So I don't think it's very useful to take "is based on" to be as broad as "is interpretable using".
Conspicuously absent in that thought is an alternative way to interpret "is based on". Because I suspect that in most senses that FP is based on lambda calculus we probably can claim it is also based on a subset of Java. Everything useful is multi-paradigm these days, programming paradigms turned out to not be a useful lens for developing useful programming languages.
That is a path-dependent property though. So if we interpret it that way we can't tell if a language is based on lambda calculus without interviewing the author.
Indeed, the definition admits that we could have two almost identical languages but only one of them is based on lambda calculus. I don't think it is a reasonable way to interpret "is based on", it requires too much knowledge of history. It is more proper to have a technical definition that is rooted in the language itself.
C'est la vie: it's always going to be a very fuzzy concept when applied, short of broadening it until it's unrecognizable. Not every property of a thing needs to be perfectly decidable with no room for guesswork.
To put it pithily, "This popular notion is provided 'as is', without warranty of any kind, express or implied, including but not limited to fitness for a particular purpose." If you really want a property that's fully intrinsic, I'd suggest disregarding fuzzy 'based on'-ness and instead considering some particular aspect you care about, e.g., "How difficult is it to express such-and-such a technique in this language?"
I don't think OOP ever had nearly as strong of a mathematical/scholarly foundation as FP has