Peter,
On Brian Lawson's list of Dissenter Baptisms 1817-1849 you will find the following:- (to which I have added the godparents in the hope that you may find a new link somewhere)

15 Nov 1844 Lynchy, Charles of Andrew Lynchy & Jane Irvine g.p's Charles Lynchey & Anne Gallagher
17 Mar 1839 Lynchey, Eleanor Of John Lynchey & Catherine Duffy g.p's Richard & Elizabeth Divine
11 July 1833 James Lynchey of John Lynchey & Catherine Duffy g.p's Charles Lynch & Elizabeth Lanaghan
29 April 1846 John Lynchey of John Lynchey & Catherine Duffy g.p's John McTague & Mary King
28 Nov 1841 Mary Lynchey of John Lynchey & Catherine Duffy g.p's Daniel Kelly & Mary Gallagher
16 May 1830 Mary Ann Jane Lynchey of Jeffery Lynchey & Susan Cannell g.p's Thomas Crelen & Mary & Eliza Mercer
13 Jun 1842 Sarah Lynchy of Andrew Lynchy & Jane Irwin g.p's Edward Collins & Eleanor Duffy
20 Mar 1837(born on 17th) Susan Lynch of John Lynch & Catherine Duffy g.p's Hugh McCartan & Margaret Christie
24 Mar 1844 Catherine Lynchy of John Lynchey & Catherine Duffy g.p's John Brennan & Mary Conroy
3 May 1835 Catherine Lynchey of John Lynchey & Catherine Duffy g.p's Peter Donnelly & Ann Collins
3 Sep 1848 Catherine Lynchy of John Lynchy & Catherine Duffy g.p's Robert Corkhill & Jane Irvine
12 Mar 1847 Lynchy James of Andrew Lynchy & Jane Irvine g.p's James McGrettin & Mary Hughes
22 July 1826 Sarah Lynchy of Michael Lynchy & Sarah Mullen g.p's James Donally & Ann Collins

The spellings I have used are from the R.C. baptismal register.

So we appear to have a Charles as godparent to John & Catherine's children and also Jane Irvine (godparent 1848)who we presume became Andrew's wife.

In1841 census we find John 28yrs( a dealer) & Catherine 25yrs, Susan 4yrs & Eleanor 2yrs in Cattle Market St Douglas.
Charles 25yrs a pedlar with Elizabeth 25yrs living with Collins family in Mill St Castletown.

Could Charles , John & Andrew have been brothers? We'll have to keep searching!