From Ancestry.com Wiki
Lemington is a town in Essex county, Vermont. It was formed in 1762 in N.H. from Orange county, though the following competing claims for its origins are Limington. The probate and court district for Lemington is Essex. For more information, contact the town at 2549 River, Lemington 05903. On the attached map, Lemington is shown as 8 in Essex county.
For information about the state of Vermont see Vermont Family History Research.