I dont recall these two having any sort of falling out during the war although maybe I am forgetting something. It is clear at least to me that at the time of the surrender at Appomattox Longstreet was probably closest to Lee as Lee asked him for his advice in that situation.
Are you at all sure these two had some falling out after the war? The thing with Longstreet I guess is that he played ball with federal authorities and a lot of ex CSA officers did not like that. Especially Jubal Early and other lost cause supporters. The sort of revisionism of Longstreet especially his role at Gettysburg came many years later. lee died in 1870 and I think the Longstreet controvery stuff happened later even up the 1950s with Freeman's works; his chapters on the second day at Gettysburg is very critical of Longstreet and I dont think it's fair.
DS Freeman: Lees Lieutenants and R.E.Lee are standard references. CLifford Dowdey wrote books on the Penninsula campaign and is a noted Longstreet basher.