I am sorry. I don't know if this was my fault or the admin's fault but the 2 options were had lived/ had been living and not have been living.
You can also see that on the title. So again the multiple choice answer is had lived?
I agree with liliput that, in the topic sentence, past continuous tense would work with when but not with before. When simple past tense and past continuous tense are used together, the simple past tense describes an action that interrupts an ongoing (past continuous) activity (Collins dictionary, 2007). When we use before, there is no interruption. Instead, the before-clause qualifies the independent clause:Why not have been living?
If I had to choose between "had lived" and "had been living" I would choose "had lived" for this sentence because of the preposition before. Compare:
"We had been living there for 10 years when we moved to..."
"We had lived there for 10 years before we moved to..."
The preposition before puts the clause clearly in the past, rather than having a direct connection with the moment of moving as when you use when. It's a subtle difference perhaps, and certainly a challenging question, but that's why the answer is "had lived" rather than "had been living".