Of the axiomatic core. But not of any programming language.
> But it turns out that this axiomatic core is too impoverished for a lot of programming.
It's not even a programming language. It's just an axiomatic core. If you try to use it for programming you must be doing something wrong.
> is writing a lexer. I don't see anything that Lisp offers you in that respect.
Lisp is a language family, not language implementation with a library, which happens to include a lexer library.
If you mean Common Lisp as a programming language with implementations, there are portable lexers.
https://github.com/lispbuilder/lispbuilder
Writing your own lexer in Lisp shouldn't be too hard. People have written applications in Lisp which includes lexer functionality.