"Long may you run" is a phrase expressing good wishes for a long and healthy life or a long journey. It can also refer to the idea of a long-term process or the enduring impact of an action.
In the context of Neil Young's song, it's an elegy for his beloved car.
- From dear Google
--------------------------------------
I don't remember when I first heard Neil Young's singing, but it was on a long driving trip somewhere in Quebec and my first reaction was: “Oh boy, he is off tune!".
Then hubby told me a story: when recording a charity song one Christmas, the producer, David Foster, pointed out that Young's vocals were flat. Instead of re-recording or adjusting his performance, Young confidently declared, "That's my sound, man!" 
Off-tune or not, I really like (most of) his songs: calm, easy going, relaxed. On hearing his "Long may you run" again last week, I felt touched and decided to check the story behind it.
Neil has a love of older cars. The song is dedicated to his 1948 Buick Roadmaster Hearse named Mort.
Neil was on his way to Toronto and Mort broke down. The next day he had picked up Mort and was on the road for an hour when Mort broke down again and limped into a parking lot. Mort was abandoned there and Neil continued to Toronto by hitchhiking. He was always wondering whatever happened to Mort.
That reminded me of my 2nd car, a white Ford Tempo I named Whitey. I bought it 2nd-hand for $1400 CAD after starting work in Ottawa and drove it for 3 years. But one day it broke down blowing big white smoke on highway 60, about a hundred kilometers away from home. Some nice people gave me and my son a ride home. I had Whitey towed back the next day and sold it to someone listed in the yellow pages.
Sorry for the long story, but here it is, "Long may you run", to Mort and Whitey and whatever the cars you may have had and have missed.
