Example code showing weird word spacing.

test-linebreaks.lisp

(in-package :cl-user)

(asdf:load-system "cl-pdf")
(asdf:load-system "cl-typesetting")

(defun test-linebreaks (&optional (data '("Here is a line with some descriptive text, enough that it needs to linewrap.  Which means lots of text if we let it use the entire page width."
					  "Line with less text, but still seeing weird spacing.")))
  (pdf:with-document ()
    (pdf:with-page ()
      (let* ((lines (tt:compile-text (:font-size 8)
		      (loop for line in data
			    do
			    (tt:format-string line)
			    (tt:new-line))))
	     (lines-position '(36 557)))
;	(break)
	(tt::draw-block lines
			(first lines-position)
			(second lines-position)
			(- (aref (pdf::bounds pdf::*page*) 2)
			   (first lines-position))
			(- (aref (pdf::bounds pdf::*page*) 3)
			   (second lines-position)))))
    (pdf:write-document "/tmp/test-linebreaks.pdf")))

I think it's because there is no paragraph style specified. Wrapping the lines in a paragraph fixes the issue as text settings like justified, centered, etc. are paragraph settings.
So the following works for me:

(defun test-linebreaks (&optional (data '("Here is a line with some descriptive text, enough that it needs to linewrap.  Which means lots of text if we let it use the entire page width."
                      "Line with less text, but still seeing weird spacing.")))
  (pdf:with-document ()
    (pdf:with-page ()
      (let* ((lines (tt:compile-text ()
                      (tt:paragraph (:h-align :center :font-size 16)
                       (loop for line in data
                do
                (tt:format-string line)
                (tt:new-line)))))
         (lines-position '(36 557)))
;   (break)
    (tt::draw-block lines
            (first lines-position)
            (second lines-position)
            (- (aref (pdf::bounds pdf::*page*) 2)
               (first lines-position))
            (- (aref (pdf::bounds pdf::*page*) 3)
               (second lines-position)))))
    (pdf:write-document "/tmp/test-linebreaks.pdf")))

I had to move the :font-size to the paragraph but it should have worked as a default setting as you wrote initially.