This seems a little different than some other similar tickets.
This is after a multi-user macOS install:
% nix-env -iA cachix -f https://cachix.org/api/v1/install
installing 'cachix-1.5'
error: opening lock file '/nix/var/nix/profiles/per-user/arya/profile.lock': Permission denied
% ls -ld /nix/var/nix/profiles/per-user/arya/
drwxr-xr-x 2 root nixbld 64 Feb 2 11:10 /nix/var/nix/profiles/per-user/arya/
I didn’t find anything searching, and I didn’t hear back on Discord, so I came here.