Lucy, 22, thinks Simon's honesty is "refreshing" and wishes he could've been on last year's series to critique her.
Speaking to us at Virgin Media's V Festival, Lucy said: "His honesty is so refreshing and I don't think there are many people in the world who are that honest.
"I would've liked to have seen Simon on last year's series especially. I'm quite an honest person myself, so would've appreciated his opinion!"
Since The X Factor, Lucy has been busy recording her debut album Join The Club, which features the song that propelled her to stardom following her first audition - 'Last Night'.
The album also features her self-penned songs 'Tea and Toast' and 'Mountains' and will be released next month. Lucy is then set to go on tour the UK and Europe in October and November. Wow!
Lucy is now recognised in the street and has a growing fan base, which still amazes her.
She said: "I do get recognised and it's mad - but really cool too! Everyone is always asking for a photo. I never say no to that!"
We spoke to Lucy backstage at the Essex leg of V Festival, held in Hylands Park in Chelmsford. The singer performed at the two-day event and rubbed shoulders with lots of famous faces.
But she admitted: "I saw Cara Delevingne in the backstage area, but I just couldn't bring myself to go over and say hello.
"I saw one of The Vaccines too and just couldn't speak. I wouldn't say it was a case of being starstruck...but they're people who you see in magazines!"
One famous face she isn't afraid to speak to his her good friend and fellow X Factor star Rylan Clark, who she formed a close bond with on the show.
"I speak to Rylan all the time," Lucy revealed. "He's very busy a lot, he works really hard on Big Brother's Bit On The Side. I'm massively proud of him."
Watch Lucy's first X Factor audition:
For all the pictures from this year's Virgin Media's Festival, check out our gallery below!
Copyright: Rex Features AKEM