I'd do the same, fire fly. There is no point in using the past perfect tense in this very example, I think. However, I'm not a native speaker, so you had better wait for some opinions of more knowledgeable people.
I think it must be lived ... moved. It could only be had lived ... moved if instead of then we had a word like when. The reason is that when creates a fixed point in time (in the past) - after that point is the simple past, and before that point is the past perfect. (Moreover, you have to use the progressive since the act of living in Ireland and the act of moving sort of occur simultaneously; that is, the former stops & the latter begins at the same time.)
We had been living in Ireland for five years when we moved to London in 2000.
You could also say:
We had lived in Ireland for five years before we moved to London in 2000.
In this case, the progressive is not used because the act of living in Ireland occurred somewhat more anteriorly to the act of moving. This one's really hard to explain - sorry.
In any case, the fact that you have then means it should definitely be lived ... moved, at least according to my ears.