.com, or any other name is fine. So, you have downloaded Server Admin (which manages DNS via the GUI)? If not, download it.
What happens when you do:
dig server.domain.com from the Lion server?
What happens when you do the same form a client who has DNS pointed to the server?
What happens when you:
dig @192.168.1.3 server.domain.com from a client where 192.168.1.3 is the local IP of the server?
You sure you didn't enable the firewall on the Lion server and not allow DNS in?
Dig and nslookup work because I bypassed the DNS issue with a hosts file on the server. I'm asking if there is a document (official Apple) that can show me how to configure the DNS. I've looked everywhere for a configuration doc to see if I've even set it up correctly. I'm about to dump DNS and install a 3rd party Linux one. This should NOT be this complicated! Postfix and Dovecot suck, too. Why didn't they just use Sendmail?!
Ok, so, given the limited information, hard to help. But I use a .com also, works fine. DNS works fine on Lion server, postfix works fine, and so does dovecot, all top notch products. It's just named (Bind) under the hood (dns), so, nothing unusual, any bind guide would be appropriate. I find sendmail inferior, but, it probably comes down to what you personally like the most. I like postfix, someone else may like another system. Both are popular. Dovercot has been used a long time on Apple server. I love that product as well, very flexible and fast.
The only "how to" would be the install guide for correctly setting up Lion server in the first place, there are some key prompts that are more difficult to change later. DNS worked as soon as the install was done, for me, there really wasn't anything to do. You manage DNS via Server Admin (download it). It took all of a minute or so to get it to work. Since it's not working for you, obviously, something has gone wrong. Would have to have way more info. Download server admin here:
Some minimal doc can be found here specifically for DNS: