I doubt you'll find an example specific to this circuit since it's a custom design. Just by looking at it seems you need to control/get state of the RTS, DSR, DTR, and CTS lines. You can do so using VISA property nodes as shown below:
You will in essence need to toggle the lines to generate the clock and data line transitions. I suppose wherever you got the circuit there probably is some code (most likely in C) that you can take a look at to see the right sequence. You might even be able to get into a DLL that you can call from LabVIEW.
If you haven't looked at it yet, you should take a look at the
I2C spec.