Viewers watched at the weekend as Simon Cowell declined to offer the singer-songwriter a place in the live shows, after watching her audition at his Judges' Houses in Los Angeles.
But, remaining upbeat, Lizzy told fans this wasn't the end.
"Thanks so much for the messages of support over the last few months," she wrote on Facebook. "Wow! It has been an amazing experience - challenging and scary, but mostly great fun!
"Looking forward to bringing you some new songs soon ... "
Lizzy's appearance on the show generated headlines around the world thanks to her famous connection: her younger brother is Robert Pattinson, star of the Twilight saga movies.
Determined not to cash in on her famous surname, Lizzy declined to tell the judges who her brother was while auditioning, meaning she made it through the process on her own talent.
Robert has, however, been a vocal supporter of his sister on the show.
He recently told ET Canada: "She is so good. Her being on that is the most exciting thing to happen to me in such a long time. I'm SO excited about it. She's really good!"
X Factor continues Saturday night on ITV1