This article might help (I can only see this snippet on FindMyPast).
Morning Herald (London), 10 May 1836: BLAKE V. LYNCH. Catholics. In contradiction of Plunket Fleeson's evidence, with regard to his wife's living and dying a Catholic, the affidavit of the Reverend Mr. Barton was introduced by Mr. John Lynch, wherein it was deposed that, when Plunket Fleeson's wife was on her death-bed, her husband ...
Added (from same article) ... daughter, Mary Anne Fleeson, as a Catholic ; that accordingly she did bring her up as a Catholic; that they both used to attend occasionally Catholic places of worship. Dr. Kiernan (now the Catholic Bishop of Clogher), who married Miss Fleeson to Lieut. Lynch ...
Another article-
True Sun (London), 10 May 1836: ... marriage, which was performed in 1810 at Enniskillen, in Ireland, by a Popish Priest. His mother was the daughter of Mr. Fleeson, a cornet and quartermaster in the 6th Dragoons. This gentleman was a Methodist, but his wife was a Roman Catholic, and the ...