I would like to suggest that perhaps Lena did not reside in an orphanage in WV, but in OH instead. I have kept your note in my file for a long time thinking I could tie Lena in to my family in Berkeley Co., but could not. Below is my findings of late.
I found a tree in Ancestry.com family trees of a person who said Lena was born on 16 September 1899 in
Warren Co., Ohio. That motivated me to look in Warren & counties near Warren Co.
In 1900, I found a Lena Freeze listed with her mother Eliza Freeze and siblings living with grandparents, Isaac Tubord/Dubord in Clinton Co., OH, which is the county next door to Warren Co.
In 1910 census, Garland Freeze, age 13, a sibling of this Lena, was a resident of the Children's home in Clinton Co., Union Twp. None of the other children from this family were housed there. This would align with Lena coming from an orphanage and living with the Nolls in 1910.
Garland was the only Freeze listed in Clinton Co., in 1910. I could not find any Dubord/Tubord family members living in Clinton Co. either. Obviously something tragic happened to cause this child to be placed in the children's home.
I can not explain how this Lena would get from Clinton Co. to Summit Co., OH, but this seems a person to investigate further.