I ended up using two threads. One for the transmit and the other for the receive controls.
I used a global variable which is used to stop the threads when the client or server is stopped. I also needed to use a timeout in both the transmit and receive thread because the recv() and readline() methods blocked the program flow which locked up the threads if the client was stopped.
With the timeout set, I could monitor the global variable and return cleanly from the thread when the client or server was stopped.
First start the LabVIEW server, then within 60 sec run the Python client. The connection will be established and you will be able to send strings between LabVIEW and the Raspberry Pi. To stop the programs, either use the Stop button in LabVIEW or CTRL+C in Python. Both methods will stop both the server and the client.
I am sure there are many methods to do what I have done here, even better, cleaner ones. My Python is all self taught and only being used for my hobbies. I am using my Raspberry Pi for what is was designed for; learning. If you can recommend a better way to do this, please let me know because I am always keen to learn something new.