Lee had a relatively quite life after the war, doing his most to ease tensions and not draw attention to himself. After living in Richmond for a while he moved to Lexington Virginia to become President of Washington College (Now Washington and Lee) a small college sharing a campus with VMI, and spent the rest of his life there, and is buried in the chapel.

He most notably did not engage in any writing or letter campaign to defend his conduct of the war, and was critical of personalities like Jubal Early and Davis who were very vocal about their opinions and attempts by Radical Republicans who supported a harsh Reconstruction. However the Lost Cause movement didnt really get going until a few years after Lee's death in 1870.

Another side note. The surrender at Appomattox was not, and was never intended to be a general surrender of CSA forces. It was only the capitulation of those forces immediately under Lee's command excluding even those cavalry forces away from Lee's main body. Grant however was very conscious of the war drawing down, and of Lincoln's wish for reconciliation, expressed both in speech at his 2nd Inaugural, and in his recent meeting with Grant and Sherman at City Point.

It was a few days later when General Joe Johnston surrendered his commands(The Carolina's, Tenn, Georgia, and his field army) to Sherman outside Raleigh, North Carolina. Sherman was told only to accept a local capitulation as well, but exceeded his authority and agreed to a surrender of all remaining CSA field forces. The deal was later rejected in DC but by that time most remaining Southern forces had already surrendered.

http://civilwarexperience.ncdcr.gov/narrative/narrative-4.htm focuses on C but speaks to the general experience of most Southern soldiers after the war.

As for their legal standing, once most men had signed their amnesty and loyalty statements they were free to go and vote. President Johnson did sign legislation excluding several classes, mostly field officers and politicians, but by 1868 even these were withdrawn and by applying for it virtually all Confederates had all their rights restored.

Broadside texts gleefully calling for the execution of Jefferson Davis were fairly common over the course of the war. Some examples: [1] [2] [3] [4] [5] [6].

I'll quote liberally from the best of these:

That herb well deserves cultivation,
Oh scatter its seed all around,—
Let it flourish in every plantation,
While Rebels and Traitors abound.
Down, down with the tyrant “King Cotton,”
King Hemp holds the rascal in check,
If you cant cure the heart that’s all rotten,
Try a bandage of Hemp on the neck.

. . .

Come, spin a strong rope for Jeff. Davis,
And a couple for Yancey and Rhett,
(For each a detestable knave is,)
Nor Pickens nor Stephens forget.
Have a cord for old false-hearted Pillow,
Have another for Letcher supplied,
Hang old Toombs, (gloomy rogue!) on a willow
And let Twiggs to an oak twig be tied.

Let Chestnut be quickly suspended
From a branch of his own name-sake tree;
Thus let every scoundrel be ended
Who shoots at the Flag of he Free.
Thus deal with the foul instigators
Of treason and treachery base,
For Hemp is the Physic for Traitors
And the Gallows is their proper place.

Obviously, these aren't serious political treatises, but perhaps they're indicative of a certain mood.