The NYTimes had an article on LBJ's legacy. The premise of the article is the legacy has been overwhelmed by Vietnam and his other achievements diminished. No doubt that is true. At the risk of being a contrarian, I'd like to argue that his legacy is secure, at least in the long term after I'm dead.
Why? Because I think Vietnam, while destructive of millions of lives and causing much agony, will ultimately appear to be a dead end, while civil rights will never appear so. Already I think I see a general downgrading of the Cold War. I think it's true that most of the US population wasn't born when the Cold War ended, and the number of people for whom it was a live issue (say those born before 1970) is diminishing.
So if the Cold War is fading, so too must Vietnam, which was seen as a battle in the Cold War. As it turned out, I think the current conventional wisdom is there was no convincing rationale for LBJ to expand our involvement. So it's a mistake for LBJ, but we don't mostly remember our presidents for their mistakes, but their accomplishments. And there I think LBJ's will only grow.