Short answer is there was a pretty remarkable wave of Civil War memorializing, in general, in the very late 19th/ early 20th centuries because veterans were dying off: and some of the statues to Lee and others were a part of that.

The veterans of the Civil War had organizations: the Grand Army of the Republic for the Union and the United Confederate Veterans in the South. The GAR had been founded almost immediately after the War, the UCV amalgamated various Confederate veterans' groups much later, in 1889. But after 1890 both groups saw more and more of their members dying, and somewhat like the attention given to the dwindling number of WWII veterans in the 1990's, there was a general conviction that memorials should be built. In its first meeting in New Orleans, the UCV called for building a statue of Jefferson Davis. The language is remarkable:

The United Confederate Veterans are men incapable of cherishing- other feelings than those of the noblest toward the common country in all its broad dominion. Their affection for each other as comrades in march, camp and battle where they enjoyed victory or suffered defeat; their admiration for their great leaders, living and dead, their pride in Southern valor; their devotion to the Heaven-favored land of the South; their purpose to proserve an impartial history and to perpetuate the glorious memories of the great war are not inconsistent with their proven fidelity to the terms of their surrender; their man- ifest appreciation of the heroism of the Union veteran; their patriotic allegiance to the Government of the United States; their enthusiastic cheers with which they greet our country's flag; their willingness to unite with all sections to build up the whole commonwealth, their resentment of any foreign invasion of the common rights or realm; and their readiness to give themselves, their sons and their fortunes in defense of this great Union of free and sovereign States. The monument which they wish to erect will be of that chaste, simple and suggestive form appropriate to the character of the Chieftain and to the sentiment of the South. As no passion prompts its construction, so no mere pride of display will be the motive of this expression of their regard. They would make that monument become the voice of the noble- hearted Southern people who will not, because of adversity, forget the chivalrous, sincere, devoted man who was their civil leader in war and their example of dignified submission in defeat.

In other words, they wanted to build a monument to Davis, but in no way have it construed as a sign they wanted a revival of the Confederate cause. However that seems difficult to argue from the present perspective, the intent was to somehow honor the veterans without making it political. From 1890, the same time, Richmond would slowly build its Monument Avenue and begin erecting statues. Lee came first, and Jackson, Jeb Stuart, Jefferson Davis were added by 1919. At the same time, monuments began to be erected on battlefields. But southern states, being much poorer than northern ones, generally built fewer and generally started later. For example, the Indiana one at Antietam, built in 1910, cost a great deal of money for the time (over $10,000) and planning and building it was a common item in Indiana papers, while the Confederate ones on the same battlefield are sometimes even centennial ones, i.e 1961. The one to Lee didn't go up until 2005 . Which is not within the 20 year rule, here, but taken as a piece of historical writing, the inscription is perhaps also remarkable:

General Lee led his troops along this road into Sharpsburg on September 15, 1862. Outmanned 2-1 he would outmaneuver the Federals on the 17th. Although hoping for a decisive victory Lee had to settle for a military draw. Robert E. Lee was personally against secession and slavery, but decided his duty was to fight for his home and the universal right of every people to self-determination.

Compared to the Longstreet statue at Gettysburg, erected around the same time as the Lee statue at Antietam:

Soldiers of Gen. Longstreet’s command held and protected the right wing of the army July 2-4 1863. His First Corps attacked and dislodged Union forces at the Devil’s Den, the Wheatfield and the Peach Orchard, on July 2. As a portion of his infantry secured the Peach Orchard, Gen. Longstreet advanced on horseback with them. The following day, Gen. Longstreet was ordered by Gen. Robert E. Lee to coordinate an attack against the Union line on Cemetery Ridge. On July 3, “Longstreet’s Assault” was repulsed with great loss after penetrating the enemy’s battle line on Cemetery Ridge. During the march back to Virginia, Gen. Longstreet and his First Corps played a prominent role in protecting the retreating army.“By the soldiers he is invariably spoken of as ‘the best fighter in the whole army.’ “- Lt. Col. Arthur J. Fremantle, Her Majesty’s Coldstream Guards June 27, 1863”

Although that statement that Lee was personally opposed to slavery and wanted self-determination for all is at least dubious, and the inscription to Longstreet more meticulously limits itself to praising him as a soldier, between the three statements by the UCV in 1889 and the groups that funded the Lee and Longstreet statues there is a shared awkwardness- how to honor someone with a statue without admitting that what they were fighting for was a bad idea. The problem is that the statues themselves become the statement: that regardless of the inscription or even the intent, simply because they are honorific they can suggest that the bad idea wasn't that bad.