  This is the help descriptor from that page, indicating that the RAC and SEL are the only components that would be sent to the syslog server. As you mentioned, the Lifecycle log catches these, but does not appear to be included in the syslog's export.   The Lifecycle controller log can be exported using the following:  If you want regular updates, you might put that into a .bat file and then schedule it to run every so often with the task scheduler, or set up a cron job, if it's a Linux environment. 
We recently configure remote syslog feature. We were doing some testing with accounts. Testing was carried out on this area which included account creation, modification and deletion for each IDRAC account. When I checked this in remote server, I did not see any events being generated for each action.  Password changes carried out by tester were also not logged in remote server. When I alter the idrac accounts, despite seeing these changes recorded under the Lifecycle Log, we don’t get anything sent to remote syslog. Under alerts we have all check boxes ticked under ‘Remote System Log’ under all 19 pages. Can you please confirm if this is by design or if we may have missed something? Thank you  
Remote syslog - Account Creation, Modification and Deletion