MARY ELLEN LOCKETT is found on the 1880 Precinct 2, Lavaca Co., Texas Census. There are only 2 children, FRANK LOCKETT, age 10, and E. D., LOCKETT, age 8, listed on this Census. That could mean that the other 2 children you mentioned have died by 1880.
On Ancestry.com there is a MATHERS/SMITH TREE, owned by "randleland", who lives in Ohio.
On this family tree, he states that FRANK LOCKETT, (son of WILLIAM and MARY ELLEN LOCKETT), born about 1870, died on Sept. 14, 1897 in Colorado Co., Texas. (no source provided)
He also lists EDWARD DAWSON LOCKETT (son of WILLIAM and MARY ELLEN LOCKETT), born Nov 1871 in Lavaca Co., Texas, married NORA BELL ADAMS on Nov. 15, 1896 in Wharton Co., Texas. EDWARD and NORA had one child, ESTHER JEAN "DOLLY" LOCKETT, born Oct 29, 1897 and died Nov. 21, 1967 in Seattle Co., Washington.
EDWARD D LOCKETT and wife, NORA are found on the 1900 Kansas City, Wyandotte Co., Kansas Census, with daughter, ESTHER, age 2.
Head of household, EDWARD LOCKETT, age 28, born Nov 1871 in Texas, married 3 years, father born in Kentucky, mother born in Texas, he rents his home, his occupation is "contractor - brick".
Wife, NORA LOCKETT, age 18, born Sept 1881 in Missouri, married 3 years, she has had 1 child, with 1 still living, parents born in Kentucky.
Daughter, ESTHER LOCKETT, age 2, born Oct 1897 in Texas.
It is not known at this time if EDWARD D LOCKETT died or he and NORA separated, but NORA married CHARLES E WILLIAMS on Oct. 6, 1902 in Jackson Co., Missouri.
There is no specific death date shown for EDWARD DAWSON LOCKETT.
The above information was taken from the MATHERN/SMITH TREE on ANCESTRY.COM.
If you subscribe to ANCESTRY, please go this tree, as there are pictures of some of these family members.
I hope this helps you in your search. Sincerely, Melinda