Lea was born in Richland, Tennessee, a small village not far from Knoxville. He attended the United States Military Academy. He graduated fifth of 33 cadets in the Class of 1831. Due to his high class ranking, he was assigned to the engineers and posted to Fort Des Moines in the Iowa Territory, serving until his resignation in May 1836. In 1837, despite his youth, he became the Chief Engineer for the state of Tennessee. He then worked for the Federal government determining the boundary between Iowa and Missouri. From 1839 to 1840, he was an assistant engineer on the Baltimore and Ohio Railroad. He became a brigadier general in the Iowa militia and then the chief clerk for the U.S. War Department.