I posted the Dave Berg parody a few months ago, but here's the whole article it comes from. NATIONAL LAMPOON started out like an adult MAD since they had almost the same audience at the beginning. It didn't help that they started out making things “funny” and their first issue had a mascot. When they hired Michael Gross as art director, he knew their parodies worked better if they resembled the real thing. Then when he left and most of the original staff left and Nixon resigned, they became less relevant or funny. Right-wing pundit P.J. O'Rourke took over and made it cohesive again but also helped turn it into the titty mag most people know it as. By then it was run by cokeheads instead of potheads.
When they were at their prime and found their own voice, they did this parody of MAD. A lot of the people behind this eventually worked for them or had worked for them in the past. This was part of their Back-to-School issue in October 1971.
They were in the same building as Marvel Comics and hired lots of their artists, who never did anything for them again. Maybe they were never paid, since owner Matty Simmons was notorious for doing that to one-time artists.
Harvey Kurtzman was a mentor to the founders of NATIONAL LAMPOON, though he didn't return the favor, not getting their brand of humor.