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Few general points about your code:

1. (while condition &body) form already treats &body as an implicit progn. There's no reason to wrap it in a progn.
2. insert accepts multiple arguments. So, you could write (insert (mapconcat ...) "\n") instead of calling (insert ...) followed by (newline).
3. Traditionally, Lisp functions use - when the name of the function consists of multiple words, so, it would be better to call zip-list, not zip_list.
4. (let (res) ...) is exactly the same as (let ((res)) ...) but shorter.
5. (setq ...) can handle multiple assignments, they are executed in order they are written, so (setq a b c a) will assign b to c. No reason to write (setq a b) (setq c a).
6. split-string has argument OMIT-NULLS that controls whether empty strings are included in the results. It would be better to rely on this argument than to post-process the results.
7. As mentioned in the comments, there's an easier, more idiomatic way to obtain all lines of text from the buffer: (split-string (buffer-string) "\n").

Finally, unless only for the sake of an exercise in writing the zip-list function, the transpose operation calls for something like vector, not a list. Below is a possible alternative which uses vectors to perform this operation:

(defun wvxvw/transpose-buffer ()
  (interactive)
  (let* ((lines (split-string (buffer-string) "\n"))
         (max-length
          (cl-loop for line in lines
                   maximize (max (length line))))
         (src (cl-coerce lines 'vector))
         (dst (cl-loop with matrix = (make-vector max-length nil)
                       with len = (length src)
                       for i below max-length do
                       (aset matrix i (make-vector len ?\ ))
                       finally (cl-return matrix))))
    (cl-loop for i upfrom 0
             for line across src do
             (cl-loop for j upfrom 0
                      for c across line do
                      (aset (aref dst j) i c)))
    (erase-buffer)
    (cl-loop for line across dst do
             (insert (cl-coerce line 'string) "\n"))))