I'm glad you're not giving up.

I looked for all women living in Halifax Co., VA with first names starting with the letters JUL and last names starting with the letters ROB. I found only one woman born after 1900.

1930 Census South Boston, Halifax Co., VA
#909 Willows
Joseph E. Heathery Head M W 23 married b. VA Father b. VA Mother b. VA Occu: truck Driver Railway Express
Virginia E. Heathery Wife F W 22 married b. GA Father b. GA Mother b. GA Occu: Saleswoman Grocieries
Love J. Heathery Dau F W 5 single b. VA Father b. VA Mother b. GA
Edwin Heathery Son M W 1 single b. VA Father b. VA Mother b. GA
Julia Robertson Servant F Neg 22 single b. VA Father b. VA Mother b. VA Occu: Servant Private Family

I searched the 1920 Census, again, I found this young woman:

1920 census Banister Dist, Halifax Co., VA
Edward Roberson Head M B 35 married b. VA Father b. VA Mother b. VA
Naomie Roberson Wife F B 25 married b. VA Father b. VA Mother b. VA
Neilmouth? Roberson Dau F B 15 single b. VA Father b. VA Mother b. VA
John H Roberson Son M B 12 single b. VA Father b. VA Mother b. VA
Julia Roberson Dau F B 11 single b. VA Father b. VA Mother b. VA
Sallie B Roberson Dau F B 6 single b. VA Father b. VA Mother b. VA
Please (or Blease?) Roberson Son M B 7 single b. VA Father b. VA Mother b. VA
Lee C? Roberson Son M B 3 single b. VA Father b. VA Mother b. VA
Mamie Roberson Dau F B 1 single b. VA Father b. VA Mother b. VA

1930 census Banister, Halifax Co., VA
Edd Robertson Head M Neg 55 married at age 30 b. VA Father b. VA Mother b. VA Occu: Farmer Gen. Farm
Nannie Robertson Wife F Neg 55 married at age 30 b. VA Father b. VA Mother b. VA
Pledge Robertson Son M Neg 18 single b. VA Father b. VA Mother b. VA Farm laborer Gen Farm
Lee Robertson Son M Neg 15 single b. VA Father b. VA Mother b. VA Occu: Farm laborer Gen Farm
Frank Robertson Son M Neg 12 single b. VA Father b. VA Mother b. VA
Maude Robertson Dau F Neg 10 single b. VA Father b. VA Mother b. VA
Sallie Judkins Boarder F Neg 17 married at age 15 b. VA Father b. VA Mother b. VA Occu: Farm laborer Gen Farm
Jim Judkins Boarder M Neg 5mon single b. VA Father b. VA Mother b. VA

There was only one black Julia Roberts, born between 1912 & 1916, recorded in the 1920 Census in VA:

1920 Census Dist 75 Hampton, Rappahannock Co., VA
William T. Yates? Head M B 72 widower b. VA Father b. VA Mother b. VA Occu: Laborer Farm
Edward H Roberts Son-in-law M B 39 married b. VA Father b. VA Mother b. VA Occu: Laborer Farm
Susie E Roberts Dau F B 33 married b. VA Father b. VA Mother b. VA
Mary V Roberts Granddau F B 9 single b. VA Father b. VA Mother b. VA
William H Roberts Grandson M B 7 single b. VA Father b. VA Mother b. VA
Florence Roberts Granddau F B 5 single b. VA Father b. VA Mother b. VA
Julia W Roberts Granddau F B 4 single b. VA Father b. VA Mother b. VA
J. P. Roberts Grandson M B 3 single b. VA Father b. VA Mother b. VA
L. D. Roberts Grandson M B 1 single b. VA Father b. VA Mother b. VA

I couldn't find a Julia or J. Roberts anywhere in VA in 1930 fitting your grandmother's description. Just the Julia above.

1930 Census Dist 2 Hampton, Rappahannock Co., VA
Susie Roberts Head F Neg 43 widow b. VA Father b. VA Mother b. VA Occu: None
Florence Roberts Dau F Neg 13 single b. VA Father b. VA Mother b. VA
William Roberts Son M Neg 12 single b. VA Father b. VA Mother b. VA
Julian Roberts Dau F Neg 11 single b. VA Father b. VA Mother b. VA
Paul Roberts (twin) Son M Neg 10 single b. VA Father b. VA Mother b. VA
David Roberts (twin)Son M Neg 10 single b. VA Father b. VA Mother b. VA
William Roberts ** Father M Neg 100 widower b. VA Father b. VA Mother b. VA Occu: None

** Probaby, actually, William Yates.

1910 Census Hampton, Rappahannock Co., VA
William T. Yates Head M B 65 widower b. VA Father b. VA Mother b. VA Occu: Farmer General Farm
Susan E Roberts Dau F B 22 married 0 yrs 0 children born b. VA Father b. VA Mother b. VA
Jim Roberts Son-in-law M B 28 married 0 yrs b. VA Father b. VA Mother b. VA Occu: Farm Laborer ????????