From Lois Burkhalter's book Gideon Lincecum, 1793-1874 (© 1965):
Lucullus' younger son, Dr. Addison Lincecum, born in Long Point on April, 1874, seven months before Gideon died, is alive at this writing. There is much of the old Gid in him. He studied at Baylor and Texas University medical schools, working his way through medical school as an engineer on trains transporting granite blocks for Galveston jetties. He graduated in 1903, and acquired six additional medical diplomas. Dr. Addison was elected a vice president of the Texas Medical Association in 1912; he went to Cuba as a physician with Roosevelt's Rough Riders; he was commissioned a Texas Ranger in 1917; he served as captain with the 36th Division in World War I. In civilian life he served on the state board of health, investigating bubonic plague in Texas; and he was mayor of El Campo, Texas, where he became a public institution: developing a long practice; serving as superintendent of a hospital and as postmaster; and conducting a weekly radio current-events forum. Dr. Addison and Letha Gandy were married in 1897. They had three children: Mrs. Ruth Crosby of Houston, Addison (Bill) of Brazoria, and Barney, with whom the doctor lives in the century-old Gandy house deep in the sandy swamp lands out of Morales in Jackson County on the Gandy Bend Road. The Addison Lincecums are a happy, gay, hospitable people and their household is much as Gideon's must have been. All the Lincecums are musical. Dr. Addison was regarded as the champion fiddle player in El Campo.