Why did general lee surrender to general grant at Appomattox Court House?

Answer 1

The terms of surrender of the Army of Northern Virginia was simply to hand in their weapons, sign the pledge to support the USA, and go home with no threat of criminal proceedings.

But this was not a formal peace treaty.

When Sherman took the surrender of the other Confederate army under Joseph E. Johnston, - after Lincoln's assassination - he thought he was speaking for the government when he offered the same terms to all Confederate troops (and presumably politicians who had been equally guilty of treason.)

This would cause certain complications.

Answer 2

Lee surrendered because his men were barefoot and starving. Grant's terms were remarkably generous - tell your men to hand in their weapons, sign the pledge of loyalty to the USA, and go home peacefully, no hangings or jailings.

Answer 3

Because his men were barefoot and starving, and many had deserted. (He only had 28,000 left). Finally, his supply-line was cut by the aggressive Phil Sheridan.