cl-cont is a library that implements closures and runs on many CL implementations. So it's not a matter of CL can't do it, CL just has to use a library to do it.
I think there are conceptual problems mixing unwind-protect-like constructs and call/cc.
The cl-cont lib appears to only support a subset of CL (in particular unwind-protect is not supported).
So cl-cont doesn't demonstrate that CL can support it, only that a restricted subset of CL can.
I don't know if it is possible to sensibly accommodate unwind-protect and call/cc in the same language, it seems smarter people than I have avoided doing so.
Scheme's dynamic-wind serves the same purpose as unwind-protect (except with entry conditions as well, since a continuation could suddenly return into your protected code), and plays nicely with continuations. I'm not sure about the details, though.
Thanks for that, pretty interesting. I guess that makes writing entry and exit conditions a little more interesting, since they could end up being invoked multiple times.