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.
