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I guess she got a reply through a message and couldn't reply back as she only had one post at the time.

I think the connection to the church parish of Sixmilebridge was that Luke was the one baptized there on 27 Apr 1837. Even though the death record states that he was 24 years old, it does mention a brother named James. James was baptized to the same parents on 19 Jan 1835.

The likely baptism for Mary was on 1 Dec 1842 in the church just north of Sixmilebridge.
https://registers.nli.ie/pages/vtls000634683_034
The father is listed as James and that was the name of Mary's second son.

My 3X great grandparents married in a Catholic church, but never bothered to register their marriage in the civil records. The reason was that she was already a few months pregnant. They did manage to register their son's birth in the civil records a few months later.

If you are looking for a name of Michael's father, I think the answer is John.

In the 1855 Griffith's valuation there are two people with the surname Gilowrie(sic): Patrick and John. That is in the townland of Ballyfaudeen.
https://www.townlands.ie/clare/corcomroe/killaspuglonane/killaspugonane/ballyfaudeen/

In 1879, Michael and Bridget have a son named John.
https://civilrecords.irishgenealogy.ie/churchrecords/images/birth_returns/births_1879/02914/2067861.pdf
In 1878, I believe they had a daughter named Ellen, but they spelled Bridget's maiden name as Scanlon instead of Neylon.
https://civilrecords.irishgenealogy.ie/churchrecords/images/birth_returns/births_1878/02938/2076513.pdf

I started from the premise that he had children in Rathernan and they were named after his parents.
Peter 15 Dec 1865
https://civilrecords.irishgenealogy.ie/churchrecords/images/birth_returns/births_1866/03544/2304558.pdf
Elizabeth 17 Jan 1864
https://civilrecords.irishgenealogy.ie/churchrecords/images/birth_returns/births_1864/03628/2339569.pdf
The mother was Margaret Whyte. The baptism of Elizabeth is in the Allen Parish.

Margaret and Patrick must have been married in a Catholic church before 1864, so you won't find the record in the civil records.

John
27 Nov 1814
according to findmypast, but it should actually be December.
https://registers.nli.ie/pages/vtls000634980_012

You can make a free account on findmypast and search their Catholic records for free.

Findmypast decided to transcribe the Catholic records and ancestry decided to do it jointly and have the records on both sites. They got unemployed people at the time to do the work for them, so the transcriptions aren't that great overall. Some records are only on findmypast and not on ancestry. Your best bet would be to buy a month on rootsireland. I have found many records on rootsireland from Limerick that weren't available on findmypast or ancestry. Rootsireland is a non-profit and get their records from various family history centers in Ireland. They had access to original records which means they tend to have better transcriptions.