On April 4, 1968, LIFE photographer Henry Groskinsky and writer Mike Silva, on assignment in Alabama, learned that Martin Luther King, Jr., had been shot at the Lorraine Motel in Memphis. The two men jumped into their car, raced the 200 miles to the scene of the assassination, and there — to their astonishment — found that they had unfettered access to the motel’s grounds; to nearby abandoned buildings from which the fatal rifle shot likely came; to Dr. King’s motel room; and to the bleak, blood-stained balcony where the civil rights leader fell, mortally wounded, hours earlier.

“I was astonished by how desolate it all was,” Groskinsky, now 79 years old, told LIFE.com when asked about the mood in the neighborhood around the motel. “Then again, everyone probably thought that the person who shot Dr. King might still be out there somewhere.”

For reasons that have been lost in the intervening decades, Groskinsky’s photographs from that eerily quiet night in Memphis — taken at the site, and on the very day, of one of the signal events of the 20th century — were not published in LIFE magazine, and the story behind them was not told. Until now.