you only need one mail server, you should have postfix already installed
mail to username will be delivered to that users mailbox
mail to
username@yourdomain.com will be delivered to that users mailbox
mail to
username@someotherdomain.com will be delivered to someotherdomain.com
if you have dns on the lan you should add the mx record
it would be good if you could have dns so this will work
ping mail
PING mail.mydomain.com (65.61.0.1): 56 octets data
64 octets from 65.61.0.1: icmp_seq=0 ttl=64 time=0.4 ms
64 octets from 65.61.0.1: icmp_seq=1 ttl=64 time=0.4 ms
64 octets from 65.61.0.1: icmp_seq=2 ttl=64 time=0.4 ms
but you could use the ip address if you have to