Depends on what you mean by "the wastelands". After all, California, where the Brotherhood originated is a wasteland as well and they've been there since the Great War in 2077.
If you mean the Capital Wasteland, they came there in 2255. See:
http://fallout.wikia.com/wiki/Timeline#2255
Well, Elder Lyons was heading up the delegation to DC - and there's no sign of Sarah's mom - so they couldn't have been in the Capital Wasteland longer than Sarah's been alive. Also, they were part of the group protecting the work at Project Purity, which was ongoing when you were born in 2258 - so unless Sarah Lyons is a lot older than she seems (or Momma Lyons is hidden away somewhere) I'd have to say that they arrived in the DC area sometime in the mid 2250's. Aha! More 50's fixation from FO3. (insert smiley here)
Sarah was born on the West Coast, before they came to the Capital Wasteland.