That's why Clojure was developed. The creator of Clojure wanted to use lisp in cooperate environment. The good thing about Clojure it runs on jvm and has access to its ecosystem.

Check out https://nubank.com.br/ they use clojure

CL is especially good for exploratory programming, which could be useful for a startup ...

If you ever want to grow, you'll either have a very resitricted pool of developers to choose from or you'll have to take on the overhead of teaching them CL on the job.

But most probably CL developers you'll be able to find, will be more skillful then an average developer on the market.

Isn't the clue in lisp the speculative idea that the program programs the program in the future?

Sure. Use it! Or not. Depending on your confidence in the language.

I'd use it in my own startup.

Lisp has been around for a long time. If adopting Common Lisp was a winning move for startups, we'd expect to see many startups adopting CL and running circles around their competition. The fact that we haven't seen that seems to suggest to me that that's not the case.