I can see it making concurrency easier, but lock-free-ness is an attribute of the data structure and the algorithms that interact with it, regardless of how easy it is to write concurrent code.

Lock-free-ness is a consequence of data being immutable in Erlang

You can avoid mutating data in C if you want to. People just don't, because mutation is so convenient and fast.

Yes, but standard C has no way to tell the compiler a variable is immutable (immutability != constness), so unless you go non-standard (and very verbose at it) Erlang is still a better tool for the job.