1st point is that several strands might result in same name !
Moore quotes:
LOONEY, CONTRACTED FROM O'Luinigh, 'Luinigh's descendant,' (luitineach, armed.')

Gillacrist O'LUINIGH, Lord of Cinel Moen,' A.D. 1090*
The O'LOONEYS were chiefs of Mulntir Loney, in Tyrone.
Compare (Irish) O'LOONEY, LOONEY.

M'LAWNEY [1504], LOWNYE [1540], LOWENY [1602], LOWNIE [1623], LEWNEY [1626], LOONEY [1644], LONEY [1681].

Jurby (vc), Marown, Lezayre, Malew, Santon, Onchan, Lonan (c), elsewhere (u).
thus the name appears in the earliest records of Mann ! = 1540 is a bit early for inquisition - the Island was still then staunchly catholic with Earl of Derby remaining catholic until late Elizabethan times (and high church later) - few records of Jews on Islandu ntil late 1750's