According to various sources, Loderick was the only son Thomas Sullivan and a woman who also had an older daughter named Mary "Polly" Workman. Her name is unknown and is referred to as the mother of Polly Workman. The older daughter became the mother of 11 of Thomas Sullivan's children. Therefore Loderick was uncle and half-brother to the other children.

Children: burial unknown
William W. Sullivan (Dec 1843 - aft 1900)
Emanuel Sullivan (Feb 1846 - Mar 25, 1891)
Willoughby Sullivan (May 1849 - aft 1910)

Originally printed in Collier's - March 17, 1945 magazine article in "The Sullivan's Hollow" by Harry Henderson & Sam Shaw. Unfolding the Bang-Bang History of Mississippi's Most Legendary Family, and how they got that way.

http://harryhenderson.com/sullivans_hollow_index1.html

...the following was written about Loderick Sullivan and his descendents.

Otherwise, things have been relatively quiet in recent years. Most of the Sullivans are as quiet and respectable as anyone you know. Few people could he more respectable than the Lod (Loderick) Sullivans, who were run out of the Hollow by Wild Bill, according to Lod's grandson, Kylie. Lod moved sixteen miles north where he built a new cabin and later a school. Most of his descendants have since turned out to be either ministers or teachers. They are known as the "preachin', teachin' Sullivans" and are regarded as something quite different from an ordinary Hollow Sullivan. They are also the branch of the family which has moved into the outside world. One is Rev. W. L. Sullivan, minister of one of the largest Baptist congregations in Natchez. Another, J. E. Sullivan, is superintendent of schools at Meadville.

"Sullivans of Sullivan's Hollow: Cousins, Friends and Neighbors" Part 1 & 2 by Granville W. Hough and Maxine Richardson Watts
Page 41
"Loderick "Lod" Sullivan ... was the only son of Thomas Sullivan and a woman who also had an older daughter named Mary "Polly" Workman. In the absence of any other surname, this woman has been referred to as "mother of Polly Workman," as the older daughter was definite that her maiden name was Workman. The older daughter became the mother of 11 of Thomas Sullivan's children. Lod was thus half uncle as well as half-brother to these children. Lod's mother had died; by the older daughter's recollection in Natchez, Mobile, or wherever she lived; then she and Lod had ridden on a big black horse to Thomas Sullivan's home about 1818. Lod grew up as one of the Sullivan children with both older and younger siblings, and with two mothers in the household. He was the only one without a mother present, but his older sister must have taken that role. Some have suggested he or his brothers resented his situatioin, but he apparently lived near his relatives most of his life. He must have been a mild-mannered fellow without any mean dispostion. His children quite readily married their cousins and into neighboring families."

Page 43
"One story told by grandson William Larrue Sullivan, son of William and Eliza, about his grandfather's funeral, was that his body was taken in an oxcart to the cemetery, but that his father was not satisified with the position of Lod's hands. The undertaker had placed Lod's left hand on top of his right, but his father, William, changed the position and put his right hand on top of the left. (GWH: I do not know the significance of this move, but it maybe a Masonic suggestion. Perhaps others have heard of it.) It is said that Lod died of Cancer."