I know the index states his name was "Lary" but after looking at the original looks more like Lacy (not Lary) Maynard. According to the census they were living on W. 141st St. in New York. After looking at the census I found this draft card; I think it must be your great-grandmother's husband.

WWI Draft Card
(Very difficult to read -- the writing is badly faded and the scan is poor)
Lacy Gawthorne? (or Ganthorne?) Maynard
Residence: #74 W 141st St, New York, NY
Age 37
DOB May 28, 1882
Negro
Nationalized Alien Resident
Occu: Blacksmith -- not occupied (unemployed)
Nearest Relative: Catherine Maynard (same residence)
Medium height, stout build, brown eyes, brown hair, broken finger on right hand
Sept 12, 1918

Index to Declaration of Intent for Naturalization: New York County, 1907-1924
about Harold Dunstao Yard
Name: Harold Dunstao Yard
Declaration
Volume: 416
Declaration Page: 173

Index to Declaration of Intent for Naturalization: New York County, 1907-1924
about Harold Yard
Name: Harold Yard
Declaration
Volume: 648
Declaration Page: 33

http://www.italiangen.org/NYCDeathresults.asp?kind=exact&Esurname=maynard&Efirst=l&StartYear=&EndYear=&B1=Submit

Surname: Maynard
Given Name: Lacy
Age: 64 y
Death Date: Aug 20 1946
Death Certificate # 18063
Place: Manhattan