Quickly

why did confederate general robert e. lee decide to invade union territory?

to remove union pressure from virginia
to protect the confederate capital
to make winning the war easier
to draw union troops from vicksburg

I'm pretty sure that would be to remove Union pressure from Virginia. Virginia was being destroyed by the Civil War and Lee, who was only fighting for the Confederacy because of his home state, which was Virginia. Because of this, he invaded Union territory to move the fighting to Union territory to protect Virginia. Hope this helps!