I often let my dog choose where we're walking and he takes it as an opportunity to update all the places he knows in town, so we end up walking a 5k loop, it's just more chaotic than when I'm leading.
I had a Husky. For me it would have been the random path of deer, rabbits, and random people's driveways. He had no sense of direction, and cared not for walking norms.
While backpacking in Ireland, my friend and I visited the small island of Inish Oirr. We had all day to explore the island so set off without any route planned. A black dog tagged along and soon started guiding our way. He would loop back and stop to wait for us at turns. We followed him blindly through the maze of stone walls. He led us to a lake, a lighthouse, and a shipwreck. He always seemed excited to show us the next landmark. We literally followed a dog from morning until sunset. It felt as though he had done this many times before. He was such a good boy.