Lynx stores a log file and crash reports within the users documents folder. These can help diagnose issues. Most of the time the problem is the antivirus software terminating the application. Lynx is testing to see if it has a network connection for the Web Search and registration and the antivirus kills the software.
Place an exclude folder within your antivirus software to ignore:
If that does not help, open a support ticket and attach the log files found in: