Most histories of LaGrange's monument state that it was erected and/or dedicated in May 1903. However, the date appears to be off by one year.
A small item that appeared in the Elyria Reporter in both the May 24 (below) and May 26, 1904 editions notes, "Hastings post No. 207, G.A.R. will dedicated the soldiers and sailors monument May 30, at 10 a. m. All soldiers in the county are cordially invited. E. G. Johnson and A. E. Lawrence are expected to be present to give the addresses."
By the way, if you're really interested in learning about the history of LaGrange, the book LaGrange Ohio – An Early History (1995) by J.R. Johnson is a great reference. There's a copy for sale on Ebay right now.
The book includes some great vintage photos from the monument's dedication ceremonies. (The Elyria Public Library had photocopies of two of the photos from the book, which I've reproduced below.)
Other material from the files of the Elyria Public Library recount an unfortunate event involving the LaGrange monument that took place in late November 1957. Vandals hurled tar on the north side of the monument and then plastered the tar with feathers.
Here is a photo (below) showing the vandalism that I believe ran in the Chronicle-Telegram on November 21, 1957.
On that same day, the Lorain Journal included a small item under the heading “Monument Given Tar, Feathers" which stated, “The LaGrange public square monument was the target of pranksters early yesterday morning when it received a coat of tar and feathers. The incident is being investigated by sheriff’s deputies, who were informed by village officials that four or five unidentified men in a car were seen loitering about the square at the time the vandalism is believed to have occurred."