"Dead Man Walking" refers to a condemned convict making his final steps towards his appointed execution.
More loosely, it refers to any man on his way past the 'point of no return' - such as a groom on his wedding day or a soldier on a suicide mission.
As for how this saying referred to your situation, it may be that a "Dead Man Walking" is allowed to have one person accompany him to his destination for comfort. This may have been what the father meant; you were there to provide comfort for your friend as she went off to meet her committment.
_________________
The mere fact that science may not yet adequately explain an object, event, or experience does not mean the immediate explanation should automatically default to a conspiratorial, extraterrestrial, paranormal, or supernatural cause.