Lincoln County is a county located in the U.S. state of Washington. As of the 2020 census, the population was 10,876, making it the fifth-least populous county in the state. The county seat and largest city is Davenport. Lincoln County was created from Whitman County in November 1883. It is named for Abraham Lincoln, the 16th president …Lincoln County is a county located in the U.S. state of Washington. As of the 2020 census, the population was 10,876, making it the fifth-least populous county in the state. The county seat and largest city is Davenport. Lincoln County was created from Whitman County in November 1883. It is named for Abraham Lincoln, the 16th president of the United States.