Carol Bennett's book "The Lanark Society Settlers" is invaluable for anyone searching Scottish settlers who came the Lanark, Ontario in 1820 & 1821. It can be purchased on-line for about $20. If you do not wish to purchase, borrow a copy through Interlibrary Loan at your local public library (if you live in Canada).
In Bennett's book she surmises that John Nichol died within a few years of arriving in Lanark, since a "Widow Nichol" is listed in the first communion of Auld Kirk congregation in 1834. To my knowledge there are no burial records, few organized cemeteries at this time. I suspect the best you can say is that John Nichol died before 1834.
Although the mark of John Nichol receiving his first government aid installment is reproduced in Bennett's book,on the list of persons who have completed settlement duties (1836), there is no listing for Ramsay Township, Concession 2, Lot 11 East which was John Nichol's allotment. There is however a John Nichol who has completed settlement duties on Dalhousie Twp., Con. 1, Lot 11 East. The Ramsay Cess [tax] Rolls 1837 list a John Nichol on Ramsay Con 2, Lot 12 East, originally granted to Duncan Ferguson. Residents on this lot are 1 male under 16, 2 males over 16, 2 females over 16. No names were recorded. On the original land Ramsay Con. 2, Lot 11 East is listed Dinnis Odriscal [O'Driscol]. If you can locate the land documents for the sons, you might find more information. I believe the land books are at Algonquin College, Perth Ontario.