Actually, the title should probably be, Lum in Disguise. Cedric enters the store to talk with Abner about the recent happenings, and why they have been hiding out. The two guys share what they understand of the convoluted situation of the diamonds, the widow, the photo mix up, and all. Lum is taken to disguising himself, and to humor him Abner and Cedric decide to play along and not recognize him.
Their prank goes well, until grandpap enters and spoils the fun. he has brought a letter, and the plot thickens.
PS: A thin disguise has been a comedy routine before on the show. At various times, when either Lum or Abner has need to hide out from the law, or someone in town who is a threat, they try to enter the store in a disguise. Everyone recognizes them, and play along, using the prank as a way of teasing them, or in giving advice that they would otherwise be unwilling to listen to.