Peter, this 1871 census record which Brian has given you must be the right Andrew. Born 1821, which would make him underage at his marriage in 1841, but too old to be transported with his mother in 1833. Born Ireland, presumably in Down like the other children, and married to a woman from Amargh:

1881 census:
Jane LYNCHY Wife (Head) W Female 60 Co Armagh, Ireland House Keeper
James LYNCHY Son U Male 34 Douglas, Isle of Man, England Marine Store Dealer
Jane LYNCHY Daur U Female 22 Douglas, Isle of Man, England Assistant In House
Andrew LYNCHY Son U Male 20 Douglas, Isle of Man, England Marine Depot (Gen Dlr)
Charles LYNCHY Son U Male 18 Douglas, Isle of Man, England Scholar
Robert LYNCHY Son U Male 14 Douglas, Isle of Man, England Scholar
Source Information:
Dwelling 2 Drinkwater St
Census Place Onchan, Isle of Man, Isle of Man
Family History Library Film 1342346
Public Records Office Reference RG11
Piece / Folio 5602 / 93
Page Number 16

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