> Strings aren't immutable in Lisp
Neither are lists. Only the empty list is immutable, and likewise empty strings. It really is a completely equivalent situation. There is no principled reason that the empty list should be unique and the empty string not.
Yes there is a principled reason. If we accept that we have a list which is recursively defined using a binary cell aggregate structure, as a right-leaning tree shape, then it is advantageous to have an atomic, unique empty list at the bottom of the recursion. That atomic empty list can be represented as a machine word. We can perform a single comparison to detect the terminator: is it that object or not? Anything else, though workable, is a gratuitous complication.
The empty string is mutable. Even the literal one is potentially mutable: you can try it at your own risk. You ca make a mutable empty string with (make-string 0) or by mutating a non-empty string.
Any mutable string can be mutated to make it empty:
(delete #\a (make-string 3 :initial-element #\a)) -> ""
It may be undefined behavior to modify "", but it's not the same thing. Suppose that mutating "" signals an error; that still leaves the problem that some other string which you are allowed to mutate can be mutated empty, yet is a distinct object from that empty string.
Moreover, though every string has "" as a suffix, it's not by way of pointing to a "" object. A unique "" wouldn't serve the role of terminator.
A language with immutable strings could intern all strings, so they are de facto symbol, and then exact string comparison is eq. That implies there is only one empty string object.