It's not clear why you can't lick your lips. (Thrillist has requested an explanation of the rule. This article will be updated with an explanation if one is provided.) Nonetheless, the rule adds a whole other element to the record attempt. You can't eat a powdered doughnut without licking your fingers. That's like not licking your fingers after eating Cheetos or not rushing to the bathroom after eating fast food.
Even during L.A. Beast's training (seen in the above video), he was disqualifying himself repeatedly for licking his lips.
In the official attempt, he manages to refrain from licking his lips, which is maybe his greatest accomplishment. Of course, eating nine doughnuts in three minutes to best the previous record of six is pretty impressive too. But he didn't lick his lips!
Guinness tells Thrillist the rule about licking lips is simply to "increase the challenge" of the record and "differentiate it from our other eating records."
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