The shape of the rally lugs where they make contact with the wheel are the same as standard lug nuts. If you have anything close to where the lug openings are enlarged that big, you have a real problem.
I'd say it's a wheel problem, not a lug nut problem. Jack up a wheel, take all the lug nuts off, then see how much play you have in any direction. With correct wheel openings, there shouldn't be much play at all.
Post some pictures of the wheel openings if you are not sure. See if they are ovaled out or worn.
I used to be indecisive. Now I'm not sure. I feel like I am diagonally parked in a parallel universe. 1968 400 convertible (Scarlet) 1976 T/A - 455 LE (No Burt) 1976 T/A New baby, starting full restoration. 1968 350 - 4 speed 'vert - 400 clone (the Beast!) 1968 350 convertible - Wife's car now- 400 clone (Aleutian Blue) (Blue Angel) 2008 Durango - DD 2008 GXP - New one from NH is AWESOME! 2017 Durango Citadel - Modern is nice! HEMI is amazing! 1998 Silverado Z71 - Father-daughter project 1968 400 coupe - R/A clone (Blue Pearl) (sold) 1967 326 convertible - Sold 1980 T/A SE Bandit - Sold
