You can start by looking on fanfiction websites like Archive of Our Own (AO3). It has a large collection of various fanfictions, and you might be able to find some that combine Twilight and Grease in a singing - related context.
One interesting story could be where the characters from Twilight are transported into the Grease universe and they start singing the classic Grease songs in their own unique ways. For example, Bella might sing 'Summer Nights' with a different kind of shyness compared to the original characters in Grease.
One possible plotline could be that Lucy has a hidden talent for singing, and in the Twilight world, she uses her singing to attract the attention of a certain vampire or werewolf. Maybe it creates a new kind of bond or rivalry among the supernatural beings.
I'm not sure of specific 'Singing with Lucy Twilight' fanfiction off the top of my head. You could try searching on fanfiction websites like Archive of Our Own. They usually have a wide variety of fan - created stories.
I'm not entirely sure as I haven't read this specific fanfic. But generally, it might be about a character named Lucy and some events related to singing that occur in the Twilight universe. Maybe it's about a new vampire or human character who has a passion for singing and their interactions with Lucy within the Twilight - inspired setting.
Another theme could be exploring the backstories of the other characters in the Grease universe. Like how Rizzo got to be the tough girl she is, with fanfiction delving into her family life or early experiences in high school that shaped her.
Sandy is also a popular choice. Her transformation from the innocent new girl to a more confident young woman gives a lot of room for creativity in fanfiction. Writers can expand on how she adapts to the new environment and her relationship with Danny in more depth.
You can try looking on popular fanfic websites such as Archive of Our Own (AO3). It has a large collection of fanfictions from various fandoms, including Twilight. Just use the search function and type in 'singing with lucy twilight fanfic' and see if it pops up.
Grease science fiction might be a very niche or even newly - coined term. It could refer to science - fiction stories that involve machinery or mechanical elements that are 'greasy' in the sense of being industrial and mechanical. Think of a story set in a steampunk - like world where the gears and engines are constantly greased, and this aspect of maintenance and the properties of grease play into the plot, such as a malfunction due to a lack of proper greasing causing a spaceship to be in danger.