Lussuria was created by the Patrons to be the "host" character for Side Dishes. If there was something that needed to be explained through narration or a scene that needed to be set up, she's basically there to facilitate that. As you can tell, she was designed to look like Jenna's Goddess form she briefly took in the dream sequence from Chapter 14. She's set up to pretty much be the only recurring character throughout Side Dishes. So far, though, she hasn't really been used much... mostly she just introduces and ends chapters.
Here's a thought... could Lussuria actually be Jenna herself from the far far future (after BCC ends), having fully embraced her power and now is using it to jack off through all time and space?