It kind of funny in fact. I had just finish watching Log Horizon and wrote a review about it 7 days before the 3rd season was announce. With the first season coming out in 2013 and the second in 2014, there had been no news of another season. Cute fact, both seasons had started in October as well.
For those who don’t know, the Light Novel Arthur was place under house arrest in 2015 for tax evasion. Although at the time there was about 10 Novels out, with the first two seasons covering the first 10. Since then volume 11, 12, and 13 was posted online with only volume 11 getting a physical release. To my understanding he is currently working on the 14th volume. The name of the 3rd season is Log Horizon: Entaku Hōkai (Log Horizon: Fall of the Round Table) matching name of the 12th novel volume.