Very good news! In less than 24 hours Twitter user ちゃかも(Chakamo) helped solve our mystery. Chakamo explains that Mendo and the others are imagining Ataru with the stereotypical characteristics of a money-lender who has come to collect Lum who was presented as collateral for a debt. The flashy kimono, thick glasses and gold teeth are all characteristics of a flashy money-lender showing off his wealth. With Lum as his collateral he can now take her as his own.
Urusei Yatsura is filled with cultural humor and puns, some of which require explanation for foreign audiences before their meaning can be understood. The American publishers of the Urusei Yatsura manga (Viz) and anime (Animeigo) have been good about including translation notes in their releases to give context to some jokes that are uniquely Japanese or were particularly 1980s in their context.
However, one joke from the manga has remained mysterious to the webmasters of Rumic World. In manga volume 18, page 64, Ataru suddenly appears wearing a kimono with Noh theatrical masks and thick glasses and tries to sleep with Lum.
(Click for full-size images. Japanese is on the left, English is on the right.)
The anime also adapts this scene in Episode 89 (Lum and Ataru, A Night Alone) around the 16:59 mark (the video below should queue to that portion). Ataru is dressed identically and has golden teeth as well.