No option.
He had run out of manpower, and his few remaining troops were barefoot and starving.
Virgina, 1865
The Unconditional Surrender
Ge. Robert E. Lee surrenderd to Gen. Grant at Appomatox, VA. There were a few other military forces that did not surrender at that time, but his surrender effectively ended the Civil War. Why did he surrender? His forces no longer had the ability to do battle.
The main causes of surrender during the American Civil War are the same reason for surrender in any other war,... one side overwhelms the other.
Unconditional Surrender
General Robert E. Lee
General Lee did not "surrender the Civil War". He surrendered his army, the Army of Northern Virginia, when it was clear that he could no longer effectively fight against the Army of the Potomac commanded by Ulysses Grant.
George W. Bush
General Ulysses S. Grant accepted the surrender of the south at appomattox courthouse.
Appomattox Court House, VA on 9 April 1865
Lincoln served as President during the Civil War. in 1864, he appointed Grant as the overall commander of Union forces. Grant accepted Lee's surrender in 1865.
The surrender of Fort Sumter