It had to be an awesome party if they got DJ Mummy to play at it!
Anyway, Miyuki and Clarissa tend to magnify each other's naughty behavior, especially when alcohol is present, and public nudity followed by sexytime right there on the DJ's stage/cenotaph is the logical outcome. They'd probably be embarrassed about this later, but everyone's attention was diverted when Lyta got in a fight with the Gorn.
Enjoy,
-D