Actually, all of these are grammatically fine. Which you use can depend on personal preference and what exactly you want to say.
There are subtle distinctions between each. "Used to live on her own" and "lived on her own" are more or less the same. "Was living on her own" is used when you want to talk about something that happened at the same time:
Ten years ago, she was living on her own when the big earthquake hit the city.
The only one that's incorrect for the context is #2. The present perfect can be used to imply either an ongoing situation or a life experience, depending on how it's presented.
She visits charity shops because she has been poor for many years. (ongoing)
She likes to donate to charities because she has been poor and knows what it's like. (life experience)
When you add a time frame (e.g. "for many years") it generally implies the situation is still true. You can use the past perfect ("had lived on her own") but this is more often used establish a temporal relationship with another event:
She had lived on her own most of her life, before she got married.