It’s been a while, but every time I’ve tried to mix higher order functions and checked exceptions in Java, I’ve found it pretty painful: there’s some annoying type checking issue around the way lambdas work in Stream.map or similar. Maybe I’ll come up with a demo when I’m back at my desk.
The lambda design team knew this was a pain point, and considered some designs that could've alleviated the problem (http://mail.openjdk.java.net/pipermail/lambda-dev/2010-June/...). I think they decided it wouldn't work well, but it's at least possible to do things here.
That said, I think the decision to do lambdas the way they did tacitly killed checked exceptions.