“built on the hill.” Omri fortified the hill and built his capital city, Samaria, there. It was so well fortified that when it finally fell to the Assyrians, it took the Assyrian army three years to siege it. Samaria so dominated the region that it became the name of the region itself as well as the name of the city.

“lord of the hill.” Here, “lord” is used of the landowner, and Shemer was the owner of the hill. The word “lord” is a grammatical plural, “lords,” but it refers to Shemer the lord.