Lyman Davis was the brother of William Davis. He took part in the Rebellion of 1837 in Upper Canada and appears on this list, dated November 1, 1838, of men who have "absconded"from the Province but are wanted for treason.
"General Summary of the cases of persons charged with High Treason, specifying the final disposal of them."
I'm guessing that Lyman has gone to New York, where his father Richard is living.