There is no indication (proof or evidence) from records that William and Matilda Martin died in LaGrange County.

I looked for other postings on this family for more/better information on this family. You identified "Emily who married an Amaziah/Amariah Gravatt/Gravott." But, you did not identify any known dates of birth...that REALLY helps distinguish one William Martin from another...or Matilday Martin. The DOB is always helpful. You found them in Lagrange in the late 1800's. I found 24 Matilda Martins in the findagrave.com buried in Indiana. But no way to prove any of them are correct, even also finding a William in the same cemetery. Do you know Matilda's maiden name?

You identified finding them in the census... Where and what year(s)? Was he owning or renting his residence? Were they living with his daughter and her husband? If so, there is not likely to be any probate records if they did not have property. Do you know if they had other children that may have been living elsewhere? Where did they come from originally, when if known? They may have gone back to live with other family members?

What was his occupation?
"IF" a farmer, William Martin on 8/1/1837 obtained quite a bunch of land in LaGrange County...but no way to determine if this is or is not the correct person, without ordering the applications.
http://www.glorecords.blm.gov/results/default.aspx?searchCri...

Neither William or Matilda Martin are identified in the LaGrange County Death Index 1882-1924.
http://www.lagrange.lib.in.us/INDEX_DEATH_1882-1924.pdf
A Charles Gravit, age 52, died April 23, 1909, nothing for the other spellings of Gravatt you identified.

Births:
http://www.lagrange.lib.in.us/INDEX_BIRTH_1882-1920.pdf
Nothing found.

Divorces:
http://www.lagrange.lib.in.us/Index%20to%20Divorces[1].pdf
a Kathryn Grovatt and Earl Grovatt, but in 1930.

No findings in Wills, Heirs,etc.

Here is the master listing of those Indices:
http://www.lcigs.org/website-resources.html
It also has indices for the 1890 Census. Since you know where they were living during the census, you might be able to find them in the 1890. The actual pages were burned in the fire at the National Archives.

In the Township Histories:

http://www.rootsweb.ancestry.com/~inlagran/1882Index.html
For the Town Of LaGrange, Part 3, is found a William Martin...not enough info there to determine if this is or is not the correct person.
In the name index is found an Aaron and Emanuel Martin...no others.