GAW,
My relative in the “Five Towns” tells me that housing in Far Rockaway proper is significantly more expensive than Lawrence. Something to do with Real Estate taxes, and the more “Yeshivish” crowd wanting to live in Far Rockaway, driving the prices up.
It’s true that Far Rockaway is more a desired location for the “Yeshivish” crowd than Lawrence, but the rest is not true AFAIK.