There is of course always more to be said, but this is a FAQ. See especially responses under "Lost Cause" by /u/Georgy_K_Zhukov, /u/The_Alaskan, this thread by /u/trb1783, and this one by /u/rittermeister .

To summarize, it was precisely because Lee was a fighting man and not a politician that made part of his reputation following the war. The Lost Cause was a reaction from southern veterans and sympathizers to recast the actions of the war - and the war's basis in preserving slavery - as a doomed but noble effort that was personified, literally, by the character of Robert E. Lee. Davis remained an advocate, if a quiet one, of southern self-governance and an opponent of the federal government and Reconstruction, even going so far as to write several books about the Confederacy, but his engagement with the subject was wonkish and reserved, amounting mostly to speeches and the aforementioned memoirs-cum-political histories.

He still remained well thought of, and five years after Appomattox, Davis was invited to give a speech at Lee's funeral. This might help illustrate one of the reason's Lee's legacy loomed so large, though: he was dead. Dead men can't write speeches or books or act outside of expectation, because they're dead. Where other southernors like James Longstreet could flaunt their tight relationship with the Reconstruction government - what men like Davis referred to as "yankee and negroe rule" - Lee was silent as a statue, and championing his memory was easy to accomplish, because Lee could do nothing to get in its way.

This is not a new phenomenon and it did not begin or end with Lee. Contenders for the antebellum presidency in the United States fought wars with pamphlets about their contributions to the national legacy, citing their service in uniform, their contributions to expanding the nation as "Indian Killers," or their efforts to stem malcontention and foreign agitation; the memory of events like the War of 1812, the Battle of Tippecanoe, the death of Tecumseh, or other entries into the history of the country became heroic topos, worked into folklore and even stage plays and poems. The Civil War was, of course, no different, except that the conflict at its heart remained contentious. Every pamphleteer of the War of 1812 was at least united in their opinion that the war deserved to have been more enthusiastically supported, and very few gave any credence whatever to the political opposition.

The legacy of the Civil War, then, was recast as a conflict that remained present in the politics of the time the memory was forged. Slavery was gone, it had been defeated, but the Confederacy had been cheated. Reconstruction was a violation, an ongoing tyranny, a betrayal of the founding principles of the country. Never mind that Confederates were traitors to that very legacy, the war had been about preserving it, right? It wasn't about slaves, it was about state's rights!

Lee, and Lee's legacy, fit this mold perfectly. He had a reputation as an honorable fellow, and stories about his loyalty to his state and not the institution of slavery, was a palatable pill for encouraging southern unity. He represented the best parts of both sides of the war; a gentleman of a legacy family in the United States and its earlier colonies, famously well-dressed even in defeat, a master tactician and brilliant commander, and a warrior dedicated to an ideal that appealed to southern sympathies and to northern sensibilities, as well.

The dubious truth value of any of these aspects is immaterial; Lee was dead, and so his reputation could be forged retrospectively, and who was there to second guess it? This was only amplified as the "Lost Cause" movement gained steam through the end of the 19th and into the 20th century. It emphasized these slightly twisted aspects of Lee's character to make him into something more like George Washington, a near-caricature of sympathetic southern-facing political ideas.

This is only a very short summary, and I encourage you to check out the FAQ section on the Lost Cause.