LaCrosse is a rural small town in Whitman County, Washington, United States. The population was 297 at the 2020 census. With the completion in 1888 of the Oregon Railroad and Navigation Company railroad line between Riparia and LaCrosse, George Dawson and his wife built a shack constructed from railroad ties. By 1889, LaCrosse had a population o…LaCrosse is a rural small town in Whitman County, Washington, United States. The population was 297 at the 2020 census. With the completion in 1888 of the Oregon Railroad and Navigation Company railroad line between Riparia and LaCrosse, George Dawson and his wife built a shack constructed from railroad ties. By 1889, LaCrosse had a population of 12. The first real store was constructed in 1899 by Tom Shobe.