I believe that Lee could have been easily elected to the U.S. Senate from Virginia once the states regained control of their electional process. His popularity in Virginia was such that, that is not outside the realms of possibility. From that platform he would have been a powerful force among the southern delegations.
Better yet, I believe that prior to the 17th Amendment to the United States Constitution, U.S. Senators were not necessarily elected by the populas. So my understanding is that "Technically" once a democrat Governor was elected for the State of Virginia that Governor could have appointed Lee to fill one of those posts had Lee been a U.S, Citizen.
However, on the other side of the coin, how many of the U.S. Presidents between U.S. Grant and Woodrow Wilson can you name without looking in a history book. Not all of those Presidents in between were Republican. Any of those Democrat Presidents of that period could have been replaced by R.E. Lee. Because the democrat party as a whole was seen as being responcible for the war, particularly southern democrats. Northern Democrats were not held much better because of the Copperhead movement. While Lee may have been a polarizing figure in the North, there were many Democrats in the north, if for no other reason that party loyality, who would have supproted a Lee candidacy, because they realize that War was War, and that Lee was doing his job better than the Union commanders were.