The LineageOS blog has an RSS feed, but they don't post updates on a regular schedule:

https://lineageos.org/feed.xml

A site called LineageOS Changelog tracks device support, but you'll have to check manually:

https://www.lineageoslog.com/

You can also find the XDA Developers forum for your device, and follow the LineageOS thread for updates:

https://forum.xda-developers.com/

Finally, for real-time updates, you can view the commits to the LineageOS repositories themselves:

https://review.lineageos.org

https://github.com/LineageOS