I am in one of the neighboring schools that you mentioned. I think Lane has about 10% more FARMS kids, slightly higher minority kids, but pretty close on the demographics. From looking at the scores, it appears that the black and hispanic groups are doing better at the neighboring schools. That is where the overall rating is going down at Lane. I think there are several apartments in Kingstowne that go to Lane and there are the affordable dwelling units right next to Chesterbrook -- that's probably where the demographics differ. I don't think Island Creek has any apartment units and I'm not sure if any of those apartments in Kingstowne (center section ) go to Hayfield or Lane.
In any case, I think the Lane is not the kind of school that is so terrible that you HAVE to send your kid to private. Lane is a decent school and the decision to go private is so costly, that I think Lane is worth trying if you are the kind of family that is open to public school. If you are considering private b/c you want a smaller, more controlled environment and that alone is worth the $30K, then you probably won't be happy with Lane just b/c it is a typical, big PUBLIC elementary school. FCPS are not "the gold standard" in my book, but I think the schools like Lane, Island Creek, and Hayfield are fine and I am satisfied with what my children are getting out of it.