Wikipedia says that Burt Lake is a 17,120 acre lake in Cheboygan County. It was named after William Austin Burt, who, together with John Mullett, made a federal survey of the area from 1840 to 1843. I know that you want to know more about William Austin Burt, and Wikipedia has it covered again:
William Austin Burt (June 13, 1792 – August 18, 1858) was an American inventor, legislator, surveyor, and millwright.
Burt was born in Worcester, Massachusetts, and lived in Michigan from 1822 until his death in 1858. He was a member of the Michigan Territorial Legislature, 1826-1827. He served as Mount Vernon’s first postmaster from 1832 to 1856. He was a Macomb County Circuit Court judge in 1833, a state legislator in 1853, and a deputy U.S. surveyor from 1833 to 1853. While surveying, he won acclaim for his accurate work on public land surveys. In 1857, Burt moved to Detroit, where he died a year later.
Among Burt’s numerous inventions were the typographer in 1829, which was a predecessor to the typewriter. He also invented the solar compass, a surveying tool used in the Michigan Survey, employed in regions that had an abundance of minerals, which would interfere with accurate readings when using ordinary instruments. While out surveying on September 19, 1844, in what is today Marquette County, Michigan, Burt discovered one of the largest iron ore deposits in the United States. A historical plaque commemorates William Austin Burt at Stony Creek, near his home in Mt. Vernon, Michigan.
On a personal note, when I was a kid my family had a cottage not far from here.