Based on the exception it looks like LDAP user password is not updated properly in LDAPSych tool so updating with proper user name and password will solve the problem.
[main] c.a.s.l.LDAPSynchronizer ERROR Connection's password is not set in config file.
java.lang.IllegalArgumentException: Connection's password is not set in config file.
Is the LDAPSync.xml file updated according to the documentation with LDAP user and password: Installing LDAP Sync (automic.com)
Configuring LDAP Sync: Configuring LDAP Sync (automic.com)