INTERNAL DNS ISSUE WITH WEBMAIL

I know this is a DNS issue but where the changes need to be made, I do not know. We have a Lotus Domino email server in which I have just configured for Domino Webmail. I can browse up the website a the following URL (example: mail.mycompany.com) from outside the network, however when I try to browse up the same URL internally (from inside the network) I have to use the IP address of the Domino server (example: 192.168.1.10). Rather than editing the lmhost file on each workstation, isn’t there a setting on the DNS server that can be made to reflect the internal IP to name?

This has been plaguing me for awhile! Thanks in advance.