Go to http://searches.rootsweb.com/htdig/search.html/http://searches.rootsweb.com/htdig/search.html/ and type in "Blagg Lubbock".
Lubbuck Co., TX birth records show:
James Luther listed as Luther B. Blagg m. Ruth Ella Dodson, parents of Patricia Ann Blagg (b. Dec. 17, 1931, Lubbock Co., TX).
Ethel listed as Dolly Ethel (an also as just Ethel) Blagg m. Horace Elson Denson, Sr., parents of Horace Elson Denson, Jr. (b. Jan. 26, 1927, Lubbock Co., TX) & Jack Denson (b. Apr. 30, 1928, Lubbock Co., TX).
Cora listed as Cora Belle Blagg m. Vivian Halbert Whitworth, parents of Franka Don Whitworth (b. Oct. 4, 1929, Lubbock Co., TX) & Marilyn Lou Whitworth (b. Sep. 1, 1937, Lubbock Co., TX).
They also show an Opal Dean Blagg m. Clifton Eugene Adair, parents of Mary Dee Adair (b. Nov. 25, 1947, Lubbock Co., TX).
And, Lester Lewis Blagg m. Neysa Iris La Grone, parents of Arthur Lynn (b. Nov. 21, 1948, Lubbock Co., TX).TX Divorce records appear to show that Arthur m. Mar. 23, 1986, to Dawn M. ___ (div. Jan. 31, 1995, Kaufman Co., TX; 2 ch. under age 18) [I've also found an address and phone number for an Arthur Blagg in Duncanville, Dallas Co., TX (Dallas Co. is adjacent to Kaufman Co.] that I think might be for this Arthur, contact me privately if you want to try contacting him]
I descend from a Cora Elizabeth Blagg (m. William Franklin 'Frank' Gilley).She is about the same age as Cora Belle Blagg and has a brother named Arthur (other siblings: Jance, Jack, Harrison).Their mother was named Molly (she later m. ___ Morgan).They went from AR > OK.Perhaps they could have passed through TX?Your Blagg family looks close, but doesn't quite match up with mine.