The singer and her husband Sam Cooper welcomed their second child on 8 January 2013.
A source said, "Marnie is a real cutie.
"Sam and Lily are ecstatic about adding another girl to the family.
"A little sister for Ethel is brilliant news to lift the January blues for the family."
Lily Allen confirmed the news on Twitter.
Quite overwhelmed by all the well wishing going on. THANKYOU everybody x x x— lilyrosecooper (@lilyrosecooper) January 10, 2013
Lily had been tweeted fams about her attempts to naturally induce labour last week.
She wrote, "3rd curry this week... nothing #cosywomb".
Allen and Cooper welcomed their first child, Ethel, in November 2011.
Congratulations Lily and Sam!
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PREGNANT LILY ALLEN FAINTS IN HARRODS
CELEBRITY BABIES 2012
BABY JOY! PREGNANT CELEBRITIES