Elope is a lovely word, especially if you leap into an elopement with an interloper. There are a whole bunch of lope-words spread around the languages of Northern Europe and they all mean pretty much the same thing: a stride, a run, a jump, a leap, a bound. There was Old English hleapan, and Dutch lopen, and Gothic hlaupan etc. It’s therefore very hard to tell where exactly elope comes from, but aloper is first found in French. Meanwhile, somebody who runs in where he’s not wanted is an interloper. He probably lopes along, and then leaps.
There used to be a punishment in the Swedish army for Very Naughty Soldiers. Basically, all the other soldiers would form two rows, leaving a long narrow passage between them. The Very Naughty Soldier would then have to run down the passage, or gata, whilst all the other soldier tried to hit him as hard as they could.
This was called the street-run or gat-lopp. But gatlopp sounds strange in English so we twisted it around and called it running the gauntlet.
Finally, there was once a proper bit of a proper wedding in Old English called the Brydlop, which literally means Bride-Run, where the wife hurried off to her new home as soon as the wedding finished.