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.
