I did a tutorial a week or so ago (it's not online yet, unfortunately) on FP in Kotlin. We wrote a little app to do IntelliSense style autocompletion on an n-gram model. The core code was purely functional and used lazyness as well.

I suspect "does Kotlin support FP" is one of those questions that's doomed to turn into a no-true-scotsman thing: whatever support is available will be considered insufficient by true FP fans :-) But it's good enough to let you write code in a typical functional style in many cases, with little cost.