After Googling some more, I found the original forum thread where it was posted, but the site where it was moved to has changed utterly and does not have the old content anywhere.
After @Valorum in the comments linked to the Lyzzy Fanclub wikia, I remembered which forum it was originally on - The 39 Clues forum. I then used the search function to search for
Lyzzy, but that yielded no results for some reason.
I then turned to Google: searching for
site:scholastic.com "lyzzy" returned the username of Lyss (InkForest13). Again, site-search failed, so I once again turned to Google:
site:scholastic.com "inkforest13", and found the list of her posts. I then scrolled through the list until I found the story - The Time Dial.................... a story by the Ozzomesauce and Ruthlyss Lyzzy. On the fourth page, I came across this post (link may or may not work):
@Layna: Depends on if you're elvish, human, Istari, or whatever.
@Chai: That's not exactly what I was referring to.
@Everyone: This story is officially now being posted on Journalister. Part 3 will be up, and I'm working on Part 4.
However, Journalister has removed all of the content from their old site and turned it into a blog, and I cannot now find the story. The Web Archive has failed as well.
The story opens with an execution:
“Loyal people of Carcinia,” he began solemnly, “we gather today to witness the continuation of the vital task our fathers began, the purging of an ancient scourge of humanity. The eradication of an evil which enslaved our ancestors and brought the world to its knees in a series of horrific wars.” His voice swelled in volume until it echoed throughout the square. “We all know the culprit: magic. And magicians were its most nefarious perpetrators.”
And the meeting with the time travelers is in chapter 2, although slightly misremembered.