Hi Carrie
I am both the Ireland Reaching Out volunteer for Moyarta parish and administrator of the FTDNA Clare Roots project.
It took me a while to find you at FTDNA, since you appear to be using your married surname there, your maiden surname at AncestryDNA, neither surname here at IrelandXO, and just your initials at GEDmatch!
You certainly have a number of distant DNA matches still living in West Clare, including one or two whose DNA kits are managed by myself (e.g. SE4420785 at GEDmatch).
There is another discussion of early Lynch emigrants from Doonaha at
https://www.irelandxo.com/ireland-xo/message-board/lynch-and-king-doona…
And there is another discussion about migrants from neighbouring parts of Clare to Canada at
https://www.irelandxo.com/ireland-xo/message-board/martin-mcnamara-and-…
to which the manager of one of your closest matching DNA kits has contributed.
In those discussions, I recommended checking the lists of those evicted in Kilrush Union during the famine years of 1845-52 for clues to emigrants in the same years.
As the local church was in Doonaha, that placename may have been used by some to refer to a wider catchment area than the townlands of Doonaha East and Doonaha West alone.
rootsireland.ie's coverage of County Clare records is very poor, but in your case the records you want just have not survived. In particular, no parish registers for Moyarta parish from before 1852 are known to have survived.
Your "Thomas (Patrick) Murray" should appear as an occupier in the Tithe Applotment Book of 17 Nov 1827 for Moyarta parish at
https://www.clarelibrary.ie/eolas/coclare/genealogy/tithe_applot/moyart…
but the only Murrys [as the name is spelled] in the parish were John in Liscroney, Marten in Moyarta East, Cornelius Snr. and Jnr. and Mich'l in Rahona East and West and an unnamed widow in Cluaincunneen. Perhaps "Thomas (Patrick) Murray" and his family were still living with his father (or mother) in a multi-generation household.
The Murray homestead in Lisheencrony on the road between Doonaha and Carrigaholt at
https://goo.gl/maps/Wm7etdTguPS2
and formerly at
http://maps.osi.ie/publicviewer/#V2,484854,652784,11,7
has been in the family since before Griffith's Valuation in 1855, in which the recently married Connor Murray occupied (no. 2a) a house and office with rateable annual valuation of 15 shillings on 51a 0r 14p.
Connor may have been a son of the John Murry in Liscroney in the TAB.
There were two Patrick Murrays residing in Rahona East in Griffith's Valuation in 1855. One was probably the subject of the death record at
https://civilrecords.irishgenealogy.ie/churchrecords/images/deaths_retu…
(Patrick Murray, widower, 95 years, farmer) and of the tombstone inscription at
http://www.clarelibrary.ie/eolas/coclare/genealogy/don_tran/graves/moya…
(IHS Erected by Michael Murray, Rahona in loving memory of his wife Hannah nee Roche died Feb 11 1946 and his father Patrick died March 23rd 1915 R.I.P.)
The other Patrick could be your ancestor.
There are several Lynch and Murray transcriptions from Kilcrona Graveyard at
https://www.clarelibrary.ie/eolas/coclare/genealogy/don_tran/graves/kil…
but none as early as you are looking for.
Knowing the source of the precise death years which you give might provide further clues.
I followed the interminable chains of links from your tree through other unsourced user-donated family trees, most of them probably infected with Ancestry's infamous shaky-leaf-hint virus, to find that Thomas Murray and Mary Crowe married in Tinryland, County Carlow, on 24 Feb 1821 and had a son James Murray baptised there on 13 Jul 1828. Internal migration across rural Ireland from Carlow to Clare in those years is almost unheard of. That journey still takes three hours today with fast cars and modern motorways for part of the route, but would have taken many days in the mid-1800s:
https://maps.app.goo.gl/Y6h2b486XvzE7CRq5
Of course it's possible that there were parallel couples in both counties who have been confused in the trees which you cite.
Your most important sources are the Canadian church and civil marriage and death records of your emigrant ancestors and their accompanying family members, and your DNA matches. Concentrate on those and ignore the wild speculation of other Ancestry customers!
Let me know if you would like to meet up when you get to Clare. You will be able to find my personal email address via GEDmatch.
Best wishes
Paddy Waldron