After getting a lot of help from the LR Support, we’ve found a solution. Posting here in case it helps anyone in the future. Mac El Capitan has been having lots of expired certificate issues on Google Chrome for the last few months. After fixing this issue, Language Reactor worked perfectly. I fixed it using this help (not the main advice but one in a comment):
HOW TO DOWNLOAD, INSTALL, AND SET THE NEW SECURITY CERTIFICATE FOR GOOGLE CHROME & SAFARI ON EL CAPITAN
This worked 100% on my 2008 Mac Pro Tower running El Capitan (extremely fast and reliable for its age, but cannot install Sierra on it).
Go to Chain of Trust - Let's Encrypt
Find the newest of this file link (first on the page)…
“Signed by ISRG Root X1: der, pem, txt”
Click on pem to download the correct one.
(I have my browser set to always download to the Desktop so I can quickly find the stuff I just downloaded, and I put it where it goes later).
Open Keychain Utility in the Applications > Utilities folder
Enter your password every time asked.
Click System (upper left).
Drag the new Security Certificate from the Desktop into the Security page in the open Keychain Window.
Double click on the new Security Certificate.
Click the little arrow next to “Trust” at the top to expand it.
Choose “Always Trust” in the menu next to “When using this certificate:”
You can choose “Always Trust” because it literally just came from the website of the company that creates the Trusted Certificates.