This is the only close Birth Index I could see for Lily ...
Births Jun 1892
Hamblet Lily W. Bromwich 6b 877
Only chance to see her will be 1901 and 1911 (latter we cant search due to T's & C's)
1901 - RG13; Piece: 2722; Folio: 92; Page: 45 West Brom; 15, Brickhouse Lane
Frances Hamblet 48 WIDOW Head of Household born West Brom, Staffs
Thomas Hamblet 21 son born Tipton, Staffs
William Hamblet 19 son ditto
Eliza Hamblet 13 dau West Brom
Lily Hamblet 9 dau ditto