I too am researching a LYNCH(E)Y family.
I am not certain as to when they came to the IoM but the husband may have been one of the garrison stationed on the Island.
There is a dissenter Baptism in July 1826 of Sarah, daughter of Michael LYNCHY and Sarah MULLEN.
My GGG grandmother Sarah LYNCHEY was transported to Australiain 1835 after a trial at Castle Rushen in 1833. A son Thomas was also transported (separately) for the same crime.
Sarah took 1 son and 2 daughters with her. Another sonwas left behind apparently because he was 8 years or older.
The son left behind may have been Andrew LYNCHEY who married at Ballaugh in 1841 with permission from his guardian William QUAYLE which may have put his birth C 1821 and certainly over 8 years when Sarah and children were sent to Australia.