By using the elimination system, I think your mother's father would have been Harold. You said she-Helen- lived with her grandmother after her parents died, ---so Hubert and Alvin were both still alive after 1920 when Helen & Howard show living with Frances, and Gerald was too young to be their father--so that leaves Harold. According to all I find, Alvin & Hubert were twins. Alvin married a Catherine Brown and they had one daughter, Jane. Hubert married a Nora and they had Hubert G. & Catherine.
SO--- Lemuel B. was b. 1842 in South Carolina to William & Nancy Lively. Both of them b. S C . By 1850 (Census) they are in Forsyth Co., GA and by 1870 they are in Fulton County GA where Lemuel died between 1920 and 1930. You can check those two Census records for Lemuel's siblings. From 1900 through 1930 the Census records show Lemuel & Frances in Fulton Co. Lemuel shows to be a "Compositor" or Typesetter for a printing company, and Frances was "artist" for an advertising company. Frances died in Cobb Co. in 1950, but residence shows as Fulton Co. Hubert died in Cobb Co. in 1972. Could not find death dates on others.