[ianl]

It's useful for lambda functions that recursively call themselves, you don't need these in practice because you wouldn't use a lambda. You would use a named function, therefore, they are almost purely theoretical aspect of Lambda Calculus. I can't think of any programming language that is purely lambda calculus.

[fexl]

Fexl http://fexl.com is essentially nothing more than a thin layer of lambda calculus on top of C, implemented using combinators.