I asked an officer of Knox Creek Heritage Center for information on the school. Her reply follows with my comment in brackets.

"That would be the Lincoln School. We are unsure when it was removed. Have asked many people. I think I could still look at assessment rolls when there were no improvements anymore.
On page 50 of the Country School Recollections II [available for sale at Price County Historical Society, Fifield, Wisconsin] is an article about that school with information from Allie Johnson and Joyce Bant. Maybe microfilm from the Bee [newspaper, Phillips, Wisconsin] 1950 would divulge some dates.
According to the article the school operation from 1906 to 1935. It was Joint District No. 2 in the town of Knox, a state graded with two rooms.
We do have a picture of the Lincoln school but have to dig it up.
More after tax time is over."