The 31-year-old singer - who also lent her vocals to the Twilight soundtrack - is set to hit the auditions this weekend at Wembley Arena in London, according to The Mirror.
"She blew them away with her husky, soulful vocals," a source told the publication. "She's different to usual X Factor contestants – she really stands out. She could go all the way."
Back in 2002, she reached 24 in the UK singles chart at the age of 18 after lending her vocals to Aurora's hit 'Dreaming'.
Lizzy - who also enjoyed chart success in 2003 when she scored a top 20 hit with club track 'Let The Sunshine In' - is thought to be keen to make it to the final without dropping her famous bro's name.
Singing in Vienna last night. Great city! pic.twitter.com/KFxjEs5y69
- Lizzy Pattinson (@LizzyPattinson) August 28, 2013
"She didn't mention she was related to him to any judges or producers," the insider added. "It's important to her she does not fall into the trap of just becoming 'Rob's sister'."
Robert is thought to be in the UK next week, meaning he could (read: probably won't) turn up to the audition to show his support.
Story continues below
The 28-year-old has also previously admitted he's a huge fan of the ITV singing talent show.
He previously told The Sun: "I know the X Factor goes against my musical beliefs and I shouldn't love it - but I do, I really do!
"I am borderline obsessed with Simon Cowell shows and spend my nights in bed watching them on my tablet."