For one, it's created and written by a Chemistry PhD researcher (Christian Schafmeister), not someone with a traditional CS background.
For another, it's one of the few languages that has ever attempted to interface with C++ at the template level - you can instantiate C++ template classes from CL, and catch C++ exceptions etc.
For yet another, he does compacting garbage collection for the C++ objects used in the CL implementation, with pointer patching and everything else.
There's a nice Google Tech Talk about it [0], that goes into both why he did this, and how he implemented this.
Dr Schafmeister is occasionally present on the LLVM Discord. The CLASP project is something else. That hour-long talk he gives on Youtube about it blew my mind.
Last I checked SBCL and CCL (both open source native compiled CL implementations) are quite a bit faster than Clasp.
However, if you are primarily e.g. calling computational chemistry libraries written in C++, Clasp is the way to go. It's the only non-C++ language implementation I know of with actually usable C++ support.
The C++/CLI compiler is definitely Windows-only. But I'm not sure whether the generated code would be, if you compile with /clr:pure (which can still handle everything except for setjmp/longjmp).
/clr:pure has been deprecated for some time now, unfortunately. But older compilers are still around...
[1] https://github.com/clasp-developers/clasp