The Arduino → xbee <-> xbee → serial LCD is a litle more complicated than that. Remember that the xbee is a 3.3V device.
So you’ll either have to use level shifters between the Arduino/xbee and the xbee/serial LCD, or run the arduino at 3.3V and be sure to get a 3.3V serial LCD (or some combination of the above).
It’s still doable, it’s just a little more complicated.
If it’s just a one-way link, then the simple 315/433MHz transmitter/receiver pairs are an option depending on the needed range. But this is then complicated by the need to have a more robust communications protocol at either end as you can’t just pipe serial data through these links. You would need to use something like VirtualWire (look in the playground) and put an Arduino (or at least a programmed ATMega168) at each end to handle the communications. If you did that you could eliminate the expensive serial LCD and just use an inexpensive base LCD module connected to the receiver Arduino.
I’m doing something very similar to this with a remotely located RFID panel. I then send the serial RFID tag data wirelessly to my home automation system.