via magazine.org
“The notorious [National Lampoon] January 1973 shot of a human hand holding a revolver to the head of a docile-looking dog, who suspiciously eyes the firearm with a sideways glance, was photographed by Ronald G. Harris and is the magazine’s most memorable cover.”
I believe this was in service to a marketing bromide (for which Google is now failing me) about ensuring magazine success by having a dog or a baby on the cover.
s a m h o c h b e r g - m e t i c u l o u s l y r a n d o m i z e d 
I remember when this came out. I was a hippie musician at the time in New England. Around the same time they had a fake cover for a magazine called "Negligent Mother" with a picture of two clueless moms drinking martinis over their backyard fence while a baby in a kiddie pool lays face down in the water. Classic ! Of course, we were stoned then so it was even funnier.