Interesting. The lake's named after Ira, but it's his wife's parents who are named. I'd say whoever provided the info for the 1912 history didn't know the names of Ira's folks [drats!] -- and got Mary's dad, Ephraim Farmer,correct but his wife was named Polly. Alida was the wife of Mary's brother, Nelson Farmer.
You and the 1912 history probably are right about Ira dying in 1871 [not 1870]. He seems to have been around 21 Jul 1870 when the Bloomfield Township census taker visited.
P.S. I checked out the Wisconsin Death Index last month.