There's an entry in your
$PATH pointing to a directory that you can't access, and you're using a version of git earlier than 126.96.36.199.
When you run
git lg git first does some setup, including adding an entry to the copy of the
$PATH that it is using. Then it tries to run the command
git-lg, so that a command would override the alias. When it does that it's getting the permission denied error shown in your output.
Older versions of git would stop at that point. Starting with version 188.8.131.52, it will treat that error the same as the command just not being found.
When you ran that as root git was able to look through all of the directories in the
$PATH, see that no
git-lg command exists, and so it would go on to use the defined alias.
To fix the problem you can upgrade to a newer version of git. The other option would be to make sure that you have permission to access all directories listed in your
$PATH, either by granting additional permissions on any that are a problem or by not including those in the list.