You question is a bit unusual, since DNS and LHhosts files have no
(direct) relationship.
In general, a DNS server doesn't "have" an LHHosts file.
DNS is about internet name resolution -- LMhosts (and WINS) is about
NetBIOS resolution. They do resolve names to IP addresses (primarily.)
If you really wish to automate NetBIOS name resolution, install a WINS
server and make the client computers WINS clients of it (too.)
If you really wish to automate LMHosts file update then do this: On each
client computer (in the ..\system32\drivers\etc directory) create a STUB
lhmosts file (create and copy it there manually the first time.)
In that file use an include (#INCLUDE \\server\share\lhmosts ) the FILE
from the server you wish to hold the master copy. See the SAMPLE
LMHosts file on each Windows machine in that same location: LMHosts.Sam
for the documentation and an example.
Most people no longer use the LMHosts file -- except for very limited and
usually temporary issues.