Your Levi may be the Levi listed below. I don't know what became of this Levi, but this is the earliest Antram family I've found in Ohio.
Thomas was a blacksmith in Logan county, and a Minister in the Society of Friends.After leaving Virginia, they first settled in Chillicothe, Ross county, Ohio.While on a visit to her mother they decided to remain in Logan county.He was twenty-five years old when he came to Logan county, settling in Zane township, on Christmas Day, 1803. He was the second white settler in Logan county, Job SHARP, his father-in-law, was the first, settling here in 1801. He preached in the Quaker meeting-house east of Zanesfield. Their son, Daniel, born 9 June, 1804, is said to have been the first white child born in Logan county.
Descendants of Thomas ANTRIM, Sr.
1 Thomas ANTRIM, Sr. Born: 1778 Burlington county, New Jersey Died: 21 December 1822
+Esther SHARP Married: 1799 Virginia Father: Job SHARP Mother: Phoebe (Dr.) HAINES
2 Esther ANTRIM
2 Ann ANTRIM
2 Rebecca ANTRIM
2 Job ANTRIM
2 Thomas ANTRIM, Jr.
2 Levi ANTRIM
2 Daniel ANTRIM Born: 9 June 1804 Ohio Died: 16 April 1879 Jefferson Twp., Logan county, Ohio Burial: New Salem cemetery, Jefferson Twp., Logan county, Ohio
+Eliza Ann 'Elle' SMITH Born: About 1814 Ohio - aged 50 in 1870 Logan county, Ohio census Died: 9 February 1900 Jefferson Twp., Logan county, Ohio - aged 86 years Burial: New Salem cemetery, Jefferson Twp., Logan county, Ohio
3 Jane ANTRIM Born: 17 April 1830 Died: infancy
3 Caroline ANTRIM Born: 4 July 1831 Ohio Died: 18 October 1908 Bur. New Salem Cem., Jefferson Twp., Logan county, Ohio
+Joel ARBEGAST Born: 7 December 1827 Berks county, Pennsylvania Died: 26 March 1898 Bur. New Salem Cem., Jefferson Twp., Logan county, Ohio Father: John ARBEGAST, Jr. Mother: Christina GRIMES
3 Wayne ANTRIM Born: 10 October 1832 Ohio
+Sarah RISNER? Born: About 1837 Pennsylvania - aged 33 in 1870 Logan county, Ohio census
3 Eliza Jane ANTRIM Born: October 1836
3 George ANTRIM Born: 21 February 1838 Ohio - aged 23 in 1870 Logan county, Ohio census Died: 1921 Bur. Zanesfield Cem. Jefferson Twp, Logan county, Ohio
+Mary Etta 'Marietta' WALTON Born: 1847 Ohio - aged 22 in 1870 Logan county, Ohio census Married: 30 May 1867 Died: 1925 Bur. Zanesfield Cem. Jefferson Twp, Logan county, Ohio Father: Nathan WALTON Mother: Eliza Ann WICKERSHAM
3 Mary Ann ANTRIM Born: 20 June 1840 Ohio Died: 20 December 1870 Bur. New Salem Cem., Jefferson Twp., Logan county, Ohio
3 Lenora ANTRIM Born: 17 May 1846
2 Joshua ANTRIM Born: About 1812 Died: 23 November 1871 Logan county, Ohio - aged 59y Burial: Darby Creek cemetery, Logan county, Ohio