No.

I expect this will be a fairly controversial comment, so I want to preface this by saying that I'm a big Lisp fan (just look at my handle). Lisp is my favorite programming language. I've been using it for nearly forty years. My first Lisp was P-Lisp on an Apple II in 1980. And I worked on Symbolics Lisp machines in the 1990s. They were very cool, but there's a reason they failed: general-purpose computing is infrastructure, and the economics of infrastructure are such that having a single standard is the most economical solution, even if that standard is sub-optimal. For better or worse, the standard for general-purpose computing is the C machine.

Because it's general-purpose you certainly can run Lisp on a C machine (just as you could run C on a Lisp machine). You can even do this at the system level. But Lisp will always be at a disadvantage because the hardware is optimized for C. Because of this, C will always win at the system level because at that level performance matters.

But that in and of itself is not the determining factor. The determining factor is the infrastructure that has grown up around the C machine in the last few decades. There is an enormous amount of work that has gone into building compilers, network stacks, data interchange formats, libraries, etc. etc. and they are all optimized for C. For Lisp to be competitive at the system level, nearly all of this infrastructure would have to be re-created, and that is not going to happen. Even with the enormous productivity advantages that Lisp has over C (and they really are enormous) this is not enough to overcome the economic advantages that C has by virtue of being the entrenched standard.

The way Lisp can still win in today's world is not by trying to replace C on the system level, but by "embracing and extending" C at the application level. I use Clozure Common Lisp. It has an Objective-C bridge, so I can call ObjC functions as if they were Lisp functions. There is no reason for me to know or care that these functions are actually written in C (except insofar as I have to be a little bit careful about memory management when I call C functions from Lisp) and so using Lisp in this way still gives me a huge lever that is economically viable even in today's world. I have web servers in production running in CCL on Linux, and it's a huge win. I can spin up a new web app on AWS in just a few minutes from a standing start. It's a Lisp machine, but at the application level, not the system level. My kernel (Linux) and web front end (nginx) are written in C, but that doesn't impact me at all because they are written by someone else. I just treat them as black boxes.

I don't want to denigrate ChrysaLisp in any way. It's tremendously cool. But cool is not enough to win in the real world.

[UPDATE] ChrysaLisp is actually doing the Right Thing with respect to its GUI by using a C-library (SDL). But it's trying to re-invent the compiler wheel (and the language design wheel) so that it can run on bare metal and "grow up to be a real Lisp machine" some day, and I think that aspect of the project is a fool's errand. There are already many Lisps that can run on bare metal (ECL was specifically designed for that). None of them have succeeding in displacing C, and I believe none ever will because the economic hurdles are insurmountable.