I think your Levi went to Illinois from Ohio. My great great grandpa was Velzer Shaw son of Henry Shaw son of William Sailes Shaw. William had a son Levi with his wife Amy Velzer Shaw.
There was also a Levi Shaw from West Lafayette who died here in 1892. He had daughters Phoebe and a Mrs Daniel Easton.
William Sailes Shaw was from New York or New Jersey and moved to ohio in the 1820s. His sons, Elijah, Cornelius and Robert were already here. He died in West Lafayette Ohio areound 1835 and should be buried in a cemetery right outside of town. We think the head stones are buried but have found a stone for a Robert and his wife. Also a stone for a child George son of C & R Shaw who we think is Cornelius and Rachel Shaw. When it cools off we plan to go back to the cemetery and hopefully discover some more stones.