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Male Asahel Lyman Click to view Asahel Lyman in the family tree

Asahel was born on February 8th, 1760.1   Asahel's father was William Lyman and his mother was Jemima Sheldon.  His paternal grandparents were Benjamin Lyman and Thankful Pomeroy. He had four brothers and three sisters, named William, Cornelius, Levi, Samuel, Rachel, Jemina and Submit.  He was the fourth oldest of the eight children.  He died in in infancy.1 

1 phelps.FTW @ Tree #1353
Further sources/citations:
World Family Tree Vol. 1, Ed. 1 @ Tree #3310, phelps.FTW, World Family Tree Vol. 4, Ed. 1 @ Tree #2332, 2332.ftw