Are there any implementations of this lambdas proposal on top of any production-quality compilers? Or are there some updates on how this is doing in committee?

It's straight from C++ which has had them since 2011.

I recently wrote some paper: https://www.open-std.org/jtc1/sc22/wg14/www/docs/n3654.pdf which also includes a short summary of issues when trying to put C++'s lambdas into C.