Atheists shouldn't be involved in lynching, according to this July 1903 editorial note from Charles Chilton Moore's atheist newspaper, the Blue Grass Blade.
A Kentucky native, Moore was opposed to the extra-legal aspect of lynching, not lynching per se. This was a fairly common moderate position at the time. He does not appear to have been bothered by the racial aspect of lynching or the legitimacy of the allegations and their dependance on racist tropes, but instead by the fact this "justice" was outside the law.
When he wrote about lynching, though, it was less to condemn the practice than it was to attack Christianity.
Here Moore, who prefers the more aggressive term "infidel" over "atheist," uses lynching to argue against Christianity's claim to morality:
At the time, between 50 and 100 people were being lynched every year.