This is just standard syslog, it has nothing to do with lockdown mode .... syslog server can be on Windows or Linux, doesn't matter.
The reason vi-logger does not work with lockdwown mode is it utilizes the vSphere API via vi-admin service account on vMA, when lockdown mode is enabled, ALL accounts are disabled except for vpxa (vCenter Agent) account to manage the ESXi host. Syslog bypasses all this which is what is recommended for shipping your logs to a remote system