Why should she justify anything? Just say that this is the look she wants to have and she wears wigs because she likes it.
I know a couple who only wear wigs or hats, no one has ever seen their actual hair and no one knows why they do this, but it’s no ones business so generally people don’t ask about it.
I’d suggest saying what you told us, Lola has a hard time growing her hair out, so she prefers to wear a wig. It’s the truth and Lola doesn’t have to out herself.
My grandmother, a cis woman with no applicable skin conditions, wore a wig for much of her teaching career until she got older because she’s always had very fine hair that wouldn’t even grow to her shoulders and she liked having long curly hair. I’d encourage Lola to tell the surface truth that she enjoys having long hair but struggles to grow it out so she wears a wig instead, just like somebody who has wavy hair may use a flat iron daily to achieve straight hair.
my cousin is a cis woman and wears wigs because she has very thin hair. thats all she has to say to your friends
also, people can wear wigs just because they like to wear wigs. She owes them no explanation. That is an answer in itself