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This is a common pattern in towns that have grown around a fortress, in many cultures. The fortress is placed on a hill, since that makes attacking it harder.
People migrate to the area, since anyone who can build a fortress has money, and get jobs there, or run businesses that sell to the fortress inhabitants. A town gradually appears, but there isn't room for it on the hill, so it is on lower ground. Hence a "Lower town."
Edit: The same process also happens for un-fortified towns built on hilltops. It is a bit slower, because the town tends to grow incrementally down the hill, but you still end up with upper and lower parts of the town.