Robert E. Lee never went to Tennessee in the immediate aftermath of the war. He was in Virginia when it ended and went back to his home there.
OTOH, the steamboat Robert E. Lee wasn’t launched until 1866, a year after the war. It was considered from the start to be an impressive ship, so there’s no reason why it would make Virgil sad even if he saw it then.
Wikipedia says that “the” was always supposed to be the lyric, but can’t be heard on the album. Leaving it out messes up the rhythm of the line, so it probably was intended.
What I think is that Robertson just chose an evocative image. Not everything in a song is based on anything that actually happened. You might as well ask if Virgil Caine existed.