I'm not familiar with LogRhythm, but as far as logs go, Lansweeper will scan the Windows logs of computer's event log. By default only error events will be scanned, however you can also scan non-error events. If need be, you can also use the eventlog only scanning target to frequently rescan the eventlog of computers: https://www.lansweeper.com/kb/127/scanning-with-scheduled-eventlog-scanning.html
How to scan non-error events: https://www.lansweeper.com/kb/128/scanning-non-error-events.html