You will need a way to share an input and an output over the one LANC pin.
Here is an example that shows how this can be done.
In this diagram, 15 is the data going to your Arduino (RX), and 17 is the data your Arduino is sending (TX.) 18 is ground.
So, wire things up as shown and connect to your two serial pins on the Arduino.
Your Arduino will probably receive its own sent data. You'll have to program around that.
Given that LANC isn't truly RS232 compatible, you may end up programming your own library to do some bit banging to implement the protocol. In that case, ignoring your echoed output is easy - just don't read the RX line while doing TX. If you find you can use some standard RS232 library, then you'll have to find another way to ignore the echo.
To just receive, you only need to connect the LANC line to your serial in on the Arduino.
To use the normal RX/TX lines on your Arduino, try following the instructions from the Arduino Serial reference. Ground is fine, and use digital pin 0 for the RX.
While looking for info on the signal levels for LANC, I found this article. Looks like someone has already gone to the trouble of figuring all this out and documenting it.