In the October to December 1858 birth index Alice Margaret Lewis, Worcester, Worcestershire, volume 6c, page 281.

England Select Births and Christenings
Alice Margaret Lewis baptized November 22, 1858, St. Peter the Great, Worcester, Worcestershire, father John Lewis, mother Minie Jane Lewis, abode Swansea

In the 1871 census “The Villa”, 17 Dudley Street, Sedgley, Staffordshire.
Head Frederick A. Homer, age 41, proprietor of lands and mines, born Sedgley, Staffordshire.
Wife Eliza Homer, age 39, born Nottingham, Nottinghamshire.
Daughter Alice Mary Lewis Homer, age 12, adopted child, born Worcester, Worcestershire.
Son Charles F. L. Homer, age 8, born Sedgley, Staffordshire.
Son John Twigg Homer, age 6, born Sedgley.
Son Frederick A. Homer, age 4, born Sedgley.
Daughter Ann Mary Homer, age 3, born Sedgley.
Son Paul A. Homer, age 2, born Sedgley.
3 servants. cook nurse and housemaid

England Select Burials
Alice Margaret Lewis, buried December 6, 1873, Sedgley, Staffordshire.

I would suggest the following scenario.
1. Frederick Augustus Homer and his wife Eliza were married in 1850.
2. I surmise since they had no children until 1863, more than 12 years later, they decided to adopt a child sometime between 1859 and 1863. Afterwards they had 9 children.
3. Alice Margaret Lewis Homer died less than a month after their 8th child, a girl, was born. I suggest they named the baby girl after the their adopted daughter. The baby was baptized 2 days after the burial of her adopted sister.
4. Sadly, the baby died about 6 months after the death of the adopted daughter.