When it happens, it is always possible to refresh and load the page, so it appears randomly.
If you want to debug this yourself from the client side, you can capture logs from the developer console and from the network. You will only see half of the picture. LWN would have the other half on their end.
Tools -> Browser Tools -> Browser Console
There are websites and videos that better explain how to use the developer console and log the messages, as this is a much bigger topic than I could explain here. You can export the entries to a text file. Keep in mind that if you are logged into their site as a member, you may have sensitive information in these logs. You can give this data to the folks at LWN and see if they can look in their logs to find corresponding entries. Remember this can have sensitive information. Only share it privately with the site administrators at LWN.The browser may not see the full picture. You can also capture the IP layer with Wireshark [1] There are also sites and videos that explain how to capture and analyze your network traffic with Wireshark. One of the things you will be looking for are FIN and RST packets that occur when you see these error messages. Reset packets can come from any device between your browser and their server. You can also use the "Expert Analyzer" tools in Wireshark to help identify anomalies. You can then give this data to the folks at LWN and see if they can look in their logs to find corresponding entries. There are also forums where people discuss network captures.