Mr. Lucky is an elderly man who gets a call from Guy Smiley, host of Dialing for Prizes Movie (First: Episode 0629). Guy asks Mr. Lucky if he knows the lucky "F" word of the day, and he correctly identifies it as "fur."
Mr. Lucky is elated to hear he's won, and when Guy says his prize consists of things covered with fur, he gets even more excited, thinking it's fur coats. However, his excitement quickly fades when Guy tells him what the prize really is: a mob of wonderful furry monsters (including Frazzle and Herry). He bolts to the studio to return them, but Guy refuses to take them back.
Incidentally, Mr. Lucky also appeared in a sketch at the movies with Ernie and Bert (also appearing in Episode 0666 like "Dialing for Prizes Movie"), where he gets exceedingly frustrated and annoyed at Ernie's constant emotional reactions during the movie (First: Episode 0627). Here, he has a higher, angrier voice, but is still performed by Jerry Nelson.