The family name 'Lyall' may originate from a Norse name 'liulfr', or be a corruption of the French 'Lyon', this latter option can be traced back to Normandy in the 1st century BC.
The earliest church record is from Brechin, where William Lyal was treasurer from 1411-1434. One William Lyell owned a tenement in Edinburgh in 1414, and a Gilbert Lyell was a juror in Arbroath in 1454.
More recently George Lyall succeded to his father's shipowning business in 1805, dying in 1853. He was MP for London in the 1830s, and his brother Alfred who lived from 1795 to 1865 was a noted phiosopher and traveller.
The earliest record I have in my family tree is my grandfather, who lived and (?) was born in Glasgow in 1870.
The name 'Lyall' is today found in the Scottish old county of Fife-just where the mane seems to have originated

Lyall Family Tree