Letitia Floyd Lewis (hereafter referred to as Letitia Lewis, to escape confusion) was one of the first from the Floyd family to convert to Catholicism, the family itself having ties to the faith through her parents, Letitia Preston (hereafter referred to as Letitia Preston) Floyd and John Floyd Jr. (hereafter just referred to as John Floyd). These two were relatively high born - Letitia Preston was the daughter of a prominent general and had a brother who was governor of Virginia from 1816-1819; through her father's connections she met her husband, John Floyd, who had family that were part of the Lewis and Clark expedition. A well, Letitia Preston and John Floyd's son would be governor from 1849-1852, and later U.S. Secretary of War in 1860. These two were certainly born and raised Protestant, and were from a part of Virginia near the Appalachian mountains that was likely very suspicious of organized religion.
Letitia and John Floyd's daughters were the first members of the family to formally convert, and were received into the Catholic Church in Richmond, Virginia, when their father was still governor there (1830-1834). It is not in Richmond, however, but in Washington that Letitia Preston and John Floyd began engaging with Catholicism. Before he was governor, John Floyd was a congressman from 1817-1829. During this time, they had two of their sons (William and Benjamin, then aged 6 and 8 in 1817) educated in Georgetown at Catholic schools, which were run by Jesuits (the Jesuits had been involved in education in this area since at least the appointment of John Carroll as the United States' first Catholic bishop in 1790, himself a Jesuit). The Floyd's must have felt some attachment to the school system and the Jesuits, as their sons would continue in education there for quite some time, attaining degrees from Georgetown College (as it was then known) in 1830 and 1832.
But it wasn't merely the school system and Jesuits that had an effect on the Floyds. They apparently became tied into the Catholic Church as well, and upon returning to Richmond (John Floyd would become governor in 1830) were influenced by a local priest, Fr. Timothy O'Brien, who was a pastor at St. Peter's Church there. St. Peter's was the first Catholic church in Richmond, officially established in 1834 but existing prior as a chapel. Of note is that according to St. Peter's Church history, the first congregants there "consisted mostly of Irish immigrants." This may have been an important cultural detail; though certainly not the reason for his initial attendance or interest (as he was raised Protestant), John Floyd's parents were of Scotch-Irish descent, and the company of Irish immigrants in a place not known for it's welcoming immigrants or Catholics, would then ostensibly not have bothered him. As it is, the family maintained a pew at St. Peter's during his time as governor, and it was at this time when his daughters converted. John Floyd apparently thought very highly of Fr. O'Brien, writing that he was "a man of talents and a respectable orator." Fr. O'Brien would continue to impact the family after John Floyd's death in 1837, continuing to meet with the Floyd family at Burke's Garden, where Letitia Preston had taken up residence, and to correspond with her late into her life.
It is rumored that John Floyd converted to Catholicism on his deathbed; he died in Letitia Lewis's home and was buried at the Lewis family cemetery long after she herself had converted and sought the services of a priest, so it is possible he received a Catholic funeral, but there is no record of it. Letitia Preston would formally convert in 1852, after years of impelling from the man who received her into the Church, bishop Richard Whelan. Bishop Whelan is another individual, apart from Fr. O'Brien, who may have had a significant impact on the family. He was a clergyman in western Virginia prior to being made bishop of Richmond in 1840. As a relatively prominent clergyman from a similar part of Virginia at a time there were very few Catholic priests in the area, it's likely he may have had some interaction with John Floyd during the latter's tenure as congressman and governor. What that is, I am uncertain, but Whelan was apparently an outspoken opponent of slavery at a time when Floyd was also an opponent of the institution, and so they may have corresponded in this regard.
Principle source for this is The Smithfield Review, "an academic publication that focuses on... the Preston family," which published two articles on the family, Governor John Floyd, Letitia Preston Floyd, and the Catholic Church, and Letitia Preston Flord: Pioneer Catholic Feminist, in 2015. One of these can be found on the Virginia Technical Institute's webpage here, while the other is hosted on a page dedicated to local history, here.