1861 census Montague Lanark
Thomas, b Ireland, 36, Weslayan Methodist
Rebecca, b Ireland 30
T W, 10
E J, 6
M E, 1
She must have died after census in 1861 as if she had died prior there would have been a note beside her name saying that she had died in the past year.
As registration didn't begin until 1869, unless you can find church records, I doubt if you will find out her cause of death.
I checked the deaths on Ancestry.ca for Rebecca but no luck.
Here is a site for cemeteries in Lanark County.http://www.rootsweb.ancestry.com/~onlanark/cemeteries/