This magnifying glass holder uses a socket which is meant to work with this locking ball and socket system:
It's for use with a 7.5 cm magnifying glass purchased from a dollar store. The lens was easily extracted from that magnifying glass by using a hacksaw to cut the rim at one location.
WARNING: The 7.5 cm lens is a little on the heavy side for the ball and socket system. Any heavier and it would probably just droop down. That's one reason I came up with the longer ball and socket joint https://www.thingiverse.com/thing:2770809. Look closely at my photograph of it in use and you'll see two of these longer joints in use. Fewer joints means fewer places it could droop.
The basic design idea for the ring that holds the lens comes from here:
I made the ring from scratch though, to make it easier to edit the mesh in Blender (I used fewer polygons).
I've printed it with only PLA. I print it with the socket down on the bed and so it needs support. The raft also helps keep it from falling down. The large amount of infill is for strength.
Note that the OBJ and STL files were exported from Blender. Cura was able to open the OBJ file but not the STL. I assume this is a Blender issue.
To insert the lens, just slide it into one side of the rim first and then into the other side. The rim is flexible enough to do that easily.