Common lisp’s typesystem is just not really as useful for this sort of thing. In particular it doesn’t have parameter used types so you can’t make eg a matrix of complex numbers. This breaks (1) a lot of the opportunity for optimisation by inlining (because you can’t assume that all the multiplications in your matrix{float} multiplication are regular float multiplications) or generic code (because you can’t have a generic matrix type and need a special float-matrix); and (2) opportunities for saving memory with generic data structures because the types must be associated to the smallest units and not the container (eg every object in a float matrix must be tagged with the fact that it is a float because in theory you could put a complex number in there and then you’d need to know to do a different multiplication operation).
I guess you could try to hack together some kind of templating feature to make new type-specific classes on the fly, but this won’t work well with subtyping. Your template goes system could probably have (matrix float) as a subclass of matrix, but not of (matrix real) or (matrix number). I think you’d lose too much in Common Lisp’s hodge-podge type system.
A big innovation of Julia was figuring out how to make generic functions and multiple dispatch work in a good way with the kind of generic data structures you need for good performance. And this was not a trivial problem at all. Julia’s system let’s you write generic numeric matrix code while still having float matrix multiplication done by LAPACK, which seems desirable.
The other thing is that Julia is a language where generic functions are a low-level thing all over the standard library whereas Common Lisp has a mix of a few generic functions (er, documentation is one; there are more in cltl2), a few “pre-clos” generic functions like mathematical functions, sequence functions and to some extent some array functions, and a whole lot of non-generic functions.