Middle Body of Fractal Vise for cylindrical symmetry type nut

If your lean screw came with a cylindrical symmetry nut, this may be what you need. 

Here is the amazon ref https://www.amazon.fr/dp/B08GS2PCR2?psc=1&ref=ppx_yo2ov_dt_b_product_details

inflated_nut.stl shows an “inflated” version of the nut used for the “cutting” with dimensions slightly bigger for the easy fit of the real one. You can compare with yours.

inflated_nut.stl  : dimensions with play : 4mm thickness 22.2mm diam main disk,  16.3mm total length.       2.5mm length smallest cyl, 9mm length 2nd small cyl. 10.35mm diam.

Tested and functional.

If your lead screw's nut looks like the photo, you may use these middle body/cap parts.