L.E. MARTIN and Aden HATCH indeed are listed in the 1910 Federal Census for Tennessee - Obion County - Union City.
She does not appear in the Tennessee Statewide Death Index for 1911, but that is not conclusive.
He appears in the World War I Draft Registration for Louisiana - Caddo County/Parish, and in:
1920 United States Federal Census
Name: Arden Hatch [Arden Halon] [Arden Botch] Age: 43 Birth Year: abt 1877 Birthplace: Tennessee Home in 1920: Shreveport Precinct 4, Caddo, Louisiana Race: White Gender: Male Relation to Head of House: Head Marital Status: Married Spouse's Name: Ester Hatch Father's Birthplace: Tennessee Mother's Birthplace: Tennessee Home Owned: Own Able to Read: Yes Able to Write: Yes Neighbors: View others on page Household Members: Name Age Arden Hatch 43 Ester Hatch 25 Aden Hatch 11 Harry Hatch 10 Richard Hatch 5 Jack Anttoye 27 Mozell Anttoye 24 Isidor Brygot 32 Ludie Brygot 22 Lee Brygot 2 6/12  Oscar R Brygot 9/12 [4/12] Evelyn Hatch 15 Reak Ruathage 3 Ozell Ruathage 8/12
Ancestry.com. 1920 United States Federal Census [database on-line]. Provo, UT, USA: Ancestry.com Operations Inc, 2010. Images reproduced by FamilySearch. Original data: Fourteenth Census of the United States, 1920. (NARA microfilm publication T625, 2076 rolls). Records of the Bureau of the Census, Record Group 29. National Archives, Washington, D.C. For details on the contents of the film numbers, visit the following NARA web page: NARA. Note: Enumeration Districts 819-839 are on roll 323 (Chicago City).
Description: This database is an index to individuals enumerated in the 1920 United States Federal Census, the Fourteenth Census of the United States. It includes all states and territories, as well as Military and Naval Forces, the Virgin Islands, Puerto Rico, American Samoa, Guam, and the Panama Canal Zone. The census provides many details about individuals and families including: name, gender, age, birthplace, year of immigration, mother tongue, and parents’ birthplaces. In addition, the names of those listed on the population schedule are linked to actual images of the 1920 Federal Census.