After extensive research at the Library of Congress, Pennsylvania Historical Society, Chester County Archives, and Swarthmore College and on site surveying of the land; I have come to the conclusion that Lewis was the father of Thomas. I base my decision on the following facts. In the will of Cadwaller Morgan dated September 10, 1711, and proven at October 10, 1711, in Philadelphia (Will Book C, p. 259); he names his brothers John and Lewis Morgan and his brother's wife Elizabeth Morgan and states she has children. Cadwaller Morgan was a stanch Quaker minister and the early Quaker records speak about his prosecution in Wales and his early entrance into Pennsylvania. Lewis and Elizabeth can not be found in any early Quaker records. The Morgan's listed on the Chester County Tax Rolls were living in a Baptist community in London Britain Township. In various publications, it states that Cadwaller, Lewis and John were sons of James Morgan, who also came to Pennsylvania. Other than the tax records in Chester County, the name Lewis Morgan does not appear. In the naming patterns that Thomas (1702 - 1774) used for his family, his eldest son is Lewis (for his father) and his second daughter is Elizabeth (for his mother). The tax records in Chester County stop for a period of time in 1740. The following is pure conjecture, based on the actual retracing of the path taken by the Morgan family. After the death of his father, James, his brother John inherits the land that his father had purchased in the Radnor Tract from Thomas and Jones (Tract Number One Records). Lewis is most probably under the age of majority when the ship lands at Bohemian Manor and his father dies. In a straight line north about 20 miles (from Bohemian Manor) is the Welsh settlement of 'Pencader' in the present New Castle County, Delaware. At that time this was part of Pennsylvania. Lewis could have lived with distant relatives or friends of the family, or could have been apprenticed. That community was Baptist, and the Welsh Tract Baptist Church still stands. After a search of the cemetery, no Morgan graves could be identified. Less than 10 miles due north is the Indian Town Settlement which William Penn purchased from the Indians in 1683. This area will become the nucleus of London Britain Township. Through this area runs a swift creek, where a large mill was established by John Evans (brother of Rodger). (In future generations, each Morgan operates a mill.) The London Britain Baptist Church still stands, with the cemetery. However, no remaining grave stones can be identified as Morgan. There is a number of graves that are unmarked, or with no remaining headstone; this is due to a flood in 1800 that carried away many tombstones.
I pretty much agree with Phebe's analysis of the situation. However, I should point out that I have seen an different father for Cadwaller Morgan than that presented here.
Sources for this individual: @S329@