What did Robert E. Lee vow to so after the Battle of Gettysburg?
I believe that Robert E. Lee vowed to resign his commission as the General of the Army of Northern Virginia
Lee is quoted as saying that the defeat and destruction of the army of Northern Virginia was all his fault. That the decision to send General Pickett's First Virginia in the failed charge on Cemetery Ridge disqualified Lee as commander of the army.
Lee subsequently did offer his resignation to Jefferson Davis. Jefferson Davis refused to accept Lee's resignation and persuaded Lee to continue to command the weakened Confederate forces.