The Threat Intelligence Service writes log files that can be used to troubleshoot its operation - lrtfmgr.log and lrtfsvc.log. The lrtfmgr log contains the results of software integrity tests. The lrtfsvc log contains records of every attempted connection and download. Any failures when trying to connect to a third party threat feed are logged here.
Log files are saved in the C:\Program Files\LogRhythm\LogRhythm Threat Intelligence Service\logs directory.