The singer was forced out of the show last weekend due to illness, saying in a statement: "I am gutted not to be able to continue on this journey but I'm not well enough to perform.
"To accept another free pass having missed last weekend would not be fair on the others in the competition. I wish them all well.
"I would like to express my thanks to everyone who has supported me. There is no way that this setback will prevent me from fulfilling my ambition.
"You'll be hearing from me again very soon."
However Lucy - who has been tipped to join this year's tour line up - was back to full health this week as she performed for a Christmas night switch on in Sheffield.
She tweeted her followers: "Getting back to doing what I love most. #bestremedy."
Performing tracks from the show as well as own songs, Lucy told the crowd: "Thank you for the support I've been getting over the last few weeks, you've been absolutely amazing."
Watch Lucy performing Beer Fear below!