William's dates of birth and death are approximate only, but he died apparently before 30 August 1850, when his wife, Mariah, and six of their children are found in the census in Grundy County, Tennessee. Mariah was the head of household ...
1850 Census of Civ. Dist. 5, Grundy Co., TN, p. 347, 30 Aug’’
Mariah Lynn, age 45, b. in Unk, $120 Pers Prop [See 1870]
Grundy County having been formed in 1844 from parts of Warren and Coffee Counties, Tennessee, and William's eldest son living in Warren County in 1850, it's possible that William was related in some fashion to Jacob Joseph Lynn of Warren County, Tennessee.
William himself is only found mentioned as the father in a Findagrave memorial for his son Thomas Jefferson Lynn. Mariah is mentioned there as Thomas's mother.