I don't know how helpful these would be to your specific searches for Simon Rarick [sic] and the LASH family, but two writers have some early Rarick stuff in books:
Westerwald to America; Palatine Families of Ireland; The Palatine Families of New York; More Palatine Families; and Even More Palatine Families -- all by Henry Z. Jones. His work is carefully documented, and invaluable to Palatine researchers. Also:
EARLY GERMANS OF NEW JERSEY -- Chambers. He doesn't have as much Rarick data, but does trace the earliest Raricks of New Jersey.
I believe Henry Jones would at least conjecture that the Raricks of New Jersey, and those of the lower Hudson Valley were inter-related in or near Hoechstenbach, Germany.