That is your interpretation of the Constitution but obviously not General Lee's. If you believe in the right to secede from the union, and you must put yourself into the mindset of the South in 1861 to be fair, that was the interpretation which was virtually unanimously held in Virginia at that time. Accepting that interpretation, means that to deny the right to secede because "you cannot claim to be fighting for some interpretation of the Constitution that allows you to reject it" is like saying you cannot be seeking to amend the Constitution when the Constitution provides for amendments. If you believe your state has the right to secede you do not believe you are a traitor.
While it is true that no amendment permits a state or part of state or collection of states to fight against the union there is no explicit prohibition against a state withdrawing either.
As to your last paragraph, Lee resigned his commission in the union army and offered his service to Virginia, not to the Confederacy. It was only later that he became part of the Confederate Army. The point is that his loyalty was to Virginia and that was his rationale for declining to accept command in the union army and for resigning his commission. When Virginia joined the Confederacy he naturally followed the lead of the state to which he was loyal.
The mindset is important in judging the character of the man. If you believe the United States is a union of states then, assuming again that the state has the right to withdraw from that union, by using force to drag a state back into the union is to wage an unjust war. It was not Virginia but South Carolina that fired first at Fort Sumter. It was Lincoln's call for volunteers to fight to compel states to return to the union that galvanized southern resistance and convinced them that the North intended to invade their country. Given Lee's mindset which was entirely congruent with the culture in which he lived (not the culture of David Brooks in New York City in the 21st century), his decision in 1861 is not "traitorous."
In any event, at the end of the war he was free and parted under the terms of the surrender granted by US Grant at Appomatox. Subsequently, he was never prosecuted for treason. Indeed, the Supreme Court of the United States required the federal government to compensate his family for improper expropriation of the Custis estate at Arlington. If Robert E Lee committed treason the United States government failed to make the most of it.
