Fleath is correct - confirm the lenses are actually "Leica Thread Mount" or "LTM" as opposed to the incompatible M39 Zenit SLR mount. In theory all LTM lenses *should* mount on all LTM-compatible cameras such as the Zorki 4, however as many have noted some lenses and some cameras have slightly different tolerances, and sometimes adjustment is required (I believe the user "lens_hacker" posts here sometimes, he has some interesting experiences adjusting/modifying lenses FSU lenses to fit on real Leicas and vice versa).
Also, I'm not aware of any Kievs that are LTM - the Kiev 1 - 4 (and possibly 5) are Contax-mount, the Kiev 88/Salyut are custom screw-mount, the Kiev 88CM, 6C and 60 are Pentacon 6 mount.