Some words are fun to say: lope is one of them. It's also fun to think about, as it means to move with a casual, striding gait. Imagine a horse cantering along with an easy lope. A pleasant image indeed.
Before 1825, the meaning of lope was in the line of a leap or springy jump. This comes from the Old Norse word hlaupa, which sounds like its English meaning, "to leap." This is similar to the Old Dutch lopen, "to run," and the Old English hlēapan, "leap," as well as the Scots loup, all related to the modern meaning: a long, striding gait with a little bounce to it.