In case you issue is that the TF 3566 is not staying closed anymore, I had the same issue after a short time (a few 1000's) and found the fine thread in the plastic to be the source of what would likely be a recurring problem, even with a replacement.
Solution: A quick trip to Canadian Tire (or any hardware store) to find a longer bolt that matched the thread and a nut to tighten it all up. Since my press is mounted on a portable bench, I tend to hold one of the 3 posts when seating the primer and had to make sure the bolt was not catching my knuckles. If you do the same, just ensure the bolt/nut does not extend where you don't want it to.
Contacting Lee will show you they are very supportive of their presses and might even ship the part(s) out for free, but if you need to use it now, the above should get you back in business for the moment. Otherwise, you can always manually turn the turret.
DanO