I'm a spinner but have never heard the term dizen before. However, I'm quite familiar with the diz, a curved plate with a small hole in it. It is used to draw unspun wool off of a comb or carder into a length of top or roving, respectively. See
http://www.joyofhandspinning.com/using-a-diz.shtml for how to use a diz. I expect the two words have related origins, probably in that the diz was used to prepare the wool that was wound on the distaff.

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Michael Quinion has a short piece on another related word bedizened (link). He also mentions another one distaff. And, that allows me to bring up a great term: spindle-whorl (aka spindle-twirl or spindle-whirl). I first heard about them at a conference when some archeologists were discussing textile production.