I'm a casual user of exim in my home network.
I have a CyrusImap server which I use to access my mail from wherever I am.
Setup
Incoming mail arrives at my ISP and is popped using fetchmail (which runs on the imap machine). It is then lmtp'ed into the imap server.
Outgoing mail is sent via a smarthost (smtp). In the event of 'local' mail hitting the smarthost, it is then forwarded to exim running on the imap server which also uses lmtp to deliver it.
I intend to allow fetchmail to deliver via smtp to the exim server.
My Alternate Exim Configuration
This uses exim on the imap host to receive the mail and forward it through a unix socket.
Domain List
domainlist local_domains = <your domains here>
Routers
localuser: driver = accept transport = lmtp_delivery
Transport
lmtp_delivery: driver = lmtp socket = /var/imap/socket/lmtp delivery_date_add envelope_to_add return_path_add user = mail