Lee was a hero of the Mexican War, distinguishing himself with with courage. He served as Superintendant of West Point and led the troops to put down John Brown’s raid on Harper’s Ferry. Lincoln offered him command of all Union armies, but he declined.
He was indeed well known and respected.
Not actually true.
Lincoln offered him a major generalship with responsibility for the defense of DC.
Lee considered it, and tried to get assurances through Francis Blair (a family friend whose son was in the Lincoln Cabinet) that his role could be purely defensive without having any obligation to invade Virginia.
When Blair told him there was no way anything like that could be guaranteed, he turned down the commission.
He was a well-regarded officer, but neither Lincoln nor Davis saw him as the truly great commander he would become, until he had already become such a general.