You probably already have this information, but just in case not, Down County Museum has "Prisoners Database:
Surname LYNCHEY
Firstname(s) Sarah
Alias / Other Names LYNCH
Religion Catholic
Age 50yrs
Date of birth c1785
Native Of Down
Children 3 male,2 female
Occupation Allwork. Feeble...
Tried Isle of Man Gaol Delivery 8 Nov 1833
Term 14 years
Crime Stealing money
Ship Mary 111 (5)
Departed London 16 Apr 1835
Arrived 6 Sep 1835
Ticket of leave 48/129
Certificate of freedom

Notes 1 male and 1 female child came to the Colony with Sarah.

1837 Muster;Aged 40 !!! Servant to Henry Fisher at Sydney.

Possible death for Sarah LYNCH in 1860 aged 75, died at Chippendale, Sydney."

Is this her son Andrew Lynchey on Brian Lawson's burials index?
LYNCHEY, Andrew 57 Bra 5 Oct 1879

There are other Lynchey burials in Braddan and Douglas. The parish register entries on LDS films might have more information than given in the index.

Maughold par regs have: "John LINCHEY 34 yrs Burial certified by Rob Gillow, RC priest of St Maughold's, Ramsey buried Apr 5 1883.

You could also try LDS films for Down RC records.

Sue