There are no Census records for Mary Phillips and her parents.
I did find the Lambert Family Tree, ancestry.com which included Mary.
Born: 1 May 1914, McCurtain County, Oklahoma
Father: Claud Phillips, b. 1887, TX
Mother: Siney Hunter, b. 1895 Choctaw Nation & d. 1918, OK.
Most larger libraries provide free access to Ancestry.com.
1900 Township 7, Choctaw nation, Indian Territory
Willie Wilson, head, b. Indian Territory, Oct 1876, Marr 1 yr
Ollie May, wife, b. MS Jan 1884
Sarah J. New, motherlaw, b. MS Nov 1853, married
Mitchel F. Phillips, brolaw, b. TX April 1880, farm laborer
Claud Phillips, brolaw, b. TX Oct 1886
Maud M. New, sislaw, b. Indian Terr, Jan 1890
John N. New, brolaw, b. Indian Terr, Oct 1893
1910 Township 3, McCurtain, OK
Charley Phillips, white, b. MS, 34, 2 marr 1 yr, general farmer
Minie, wife, white, b. AR, 18, 1st marr
Robert, son, Indian, b. OK, 9
Lena, dau, white, b. OK 3/12ths
Suzy Hunter, Indian, stepdau, b. OK, 14
Claud Phillips, white, brother, b. TX, 23, general farmer
I think Suzy is Siney Hunted in the Lambert Family Tree.
Born: 6 Oct 1885
Residence 1918: McCurtain Co., OK
Nearest Relative: Mrs. Effie Phillips, wife
Claud married Siney/Suzy 1910 or later, she had two daughters Josephine and and Mary and died in 1918.That's the working theory from the Lambert Family Tree.
You can contact the Oklahoma State Dept Health, www.ok.gov/health/Birth_and_Death_Certificates/ and request a copy of Mary's birth certificate. There are restrictions which are explained at their web site.
You can contact the McCurtain County Clerk, PO Box 1078, Idabel, OK 74745, 580-286-7428 and ask if they have birth documents back to 1914.
Oklahoma doesn't pubish a death index but according to the Lambert Family Tree, Mary Phillips Lambert died 18 Nov 2000, Isabel, McCurtain, OK. Do you have a copy of her obituary? Info about her parents might be in it.
If you don't have a copy of her obit, contact the McCurtain County Genealogical Society, www.rootsweb.ancestry.com/~okmcgs/index.html. Coincidentally, they are located in the same town that Mary spent most of her life.