The problem as I see it is the type for lst.

Common Lisp has a (CONS α β) type for cons cells with member types α and β, but its LIST type is defined as (OR (CONS T T) NULL), basically more of a binary tree type, where T is the Common Lisp "any" union of all types.

A useable (LIST α) type would be something like μβ.(OR (CONS α β) NULL), but that's not expressible within standard Common Lisp. I expect it to very hard to infer too, especially with CONS cells being mutable.