Breathe Again Toni Braxton
Lily has named her baby Ethel Mary, according to her mother.
The 'Smile' singer's film producer mother Alison Owen apparently revealed the name of her daughter's baby in a post on Facebook over Christmas.
Alison told the name to a friend on the social networking website and it has since been published by The Sun.
Lily gave birth to her first child with husband Sam Cooper in November last year.
The new arrival came one year after Lily suffered a miscarriage while six months pregnant in November 2010.
The singer has remained tight-lipped about the baby, but did thank her fans for their "very touching" messages of support shortly after the birth.