As Per your Question , it's seems to me , there might be block Port UDP 53 for LAN Segment, So you can easily check , just Disable IPtables Service and Check it. Just Make Sure in Client Side DNS Should be Configured.
For Better Solution for DNS Setup Options as below :
You can use Public DNS in Your LAN eg. 126.96.36.199 , then your client Machine Can Reach to your Server.
Note:- This Option you might don't wont to use , because you may be restrict Client
if You are Using Internal/Intranet DNS Server in your LAN
In DNS there is concept/configuration like Internal Views and External Views
means in your local dns you have configure as Below
if match Clients is your LAN Segment, then DNS Server will resolve Internal IP , then your can Clients can access webpage in LAN on LAN IP of your webserver.
if not match then DNS client answer Public IP.
Access this page for the same.
For troubleshooting you can use below command from client side
Or you can specify Server too as below :
dig myftp.org @address_of_your_lan_dns_or_check_using_public
If DNS Is Properly Resolving then check Port 80(http)/21(ftp) open or not using :
telnet myftp.org 21
Or In linux
nc -zvw1 myftp.org 21