Short answer: no, but you need to make sure you don't overwhelm the poor server, and you need to consider and performance issues.
Long answer: Depends what you mean by LAN. If you mean a network of computers where you might have multiple smaller networks inside (subnets, vlans, etc...) then, no. You would need to have default gateways for each division so that It could find it's way to the DNS server, but you don't need one in each piece. The caveat to that is that if you have too many devices trying to reach one main server, or you have a DNS server very far away from some clients, you will have bad performance on those clients.
The point of being far away from clients brings up another point: Though it is possible to run one DNS server and something like a VPN or a frame relay connection to join a satellite network, you will see a significant performance drop for those accessing it over the WAN connection. Therefore, though it is possible, it is not recommended. Suggested to have at least one DNS server per physical location, sometimes more depending on how many lookups you need to do/ how many machines you have.
If you have DNS servers connecting over WAN connections or leased connections (anything you dont own/ pay for bandwidth on) you also want to consider how often you replicate your servers and when. replicating in the early morning time you often get much better speeds (sometimes even bursting above your named speed) and the bandwidth averages out better (less of a peak from early morning traffic + replication than regular traffic + replication) You also want to consider that you should consider security between the servers for the replication. Frame relay, VPN, just plain authentication for the DNS replication, something. Otherwise anyone could tap your lines and find out lots of lovely internal IPs.