I recently have learned something new regarding Lotus Notes and replication: If you are using a local mail file then a replication can be triggered by the server if new mail is arriving on the server.
To achieve this you have to set “Local, then server” as the option for mail addressing in your location document. In addition you need to have an open connection to the home/mail server, so this might not work if you did not connect to your server for a longer time and the session has already timed out.
This already works since Notes 6.0 (although it was broken in 6.5.3).
Lotus Notes: Immediate Replication