Lily was also my great-grandmother's name ,@Hattiehoops - as others have said, it's a classic name for a reason.
I also know three other Lily's, though, outside of the family. One is 16 and my son's girlfriend, the second is 7 and a friend's daughter and the other is 3 and my daughter's goddaughter. When my son (17) was born, one of the other babies born that night was Lillie - I remember one of the midwives commenting on how she'd have an easier time of learning to write her name "because it's all straight lines".
Other small girls I know are Fleur, Florrie (short for Florence), Rosie, Lexi-Mai, Eloise, Francesca (x2), Ivy, Poppy, Caitlin, Ruby, Elise, Harper, Mia, Eliana (Eli for short), Anna (x2), Ella, Kristina, Millie-Bea, Sia-Rose, Abby (x2), Chloe (x2), Emily, Sophia (x2) and Lola.
Ivy is the sister of the 3 year old Lily, whilst Poppy is sister to the 7 year old.
Weirdly the two Abby and Chloes... are sisters (ie, friend A has Abby & Chloe, as does friend B). It can be confusing at times.