Hi Marie,
I have found an extended family of LYNCHEYS in the Portaferry area of County Down, with neighbours named MULLAN. Amongst the Christian names are John, James, Michael, Henry Hugh and George while the MULLANS have several Charles.
One James was deep in debt in the early 1820's and the IoM could have been an escape.
Given the statement on Sarah's entry on the Mary III indent I doubt that those you suggested were brothers they could well have been related.

Cheers

Peter