If you have Leia at Green heart or higher, she will ask you if she can spend the Star Festival at your house. If you agree, you need to attempt to leave your house at 6.00 p.m. or later on the night of 24 Winter in order to trigger the event.
She will tell you that Daryl brought her 'in return for some food' but ask that you take her home. The idea that Daryl would perform in return for food makes him sound like some sort of animal, rather than an eccentric scientist... Why should Daryl not have been invited to join you in any case? The Star Festival essentially is a family festival and Daryl would be considered the closest Leia has to family in the Valley.
This event is very much the same as the event with Leia in the original HM DS but in that game, you were a boy and strong enough presumably to carry a hefty mermaid in your arms. In Cute, the idea of carrying Leia all the way back to Daryl's basement is a little daunting... but you are not given any alternative presumably.
As with the Witch Princess, when Leia asks about food, she will discover that you have prepared none at all and she will be forced to cook for the occasion. The results are not displayed on the table. The screens go dark before the food actually materialises!