As DHCP works primarily via network broadcasts, it will only work if both the client and the server is located on the same network segment. Unless you have a Relay Agent set up, that is.

A DHCP Relay Agent is a small server that resides on one of the hosts (or directly on the router) on the client's segment, listening for DHCP requests, and forwarding them transparently to the DHCP server on the other LAN.

Since the different LANs have their own series of IP addresses, the DHCP server needs to be set up with a separate scope for each LAN served.