If you just want to run LabVIEW and have it load a VI then you just need to issue a command line command like the following:
C:\Program Files\National Instruments\LabVIEW 8.2\LabVIEW.exe pathtomyVI\myVI.vi
This will launch LabVIEW and automatically load "myVI.vi". It's the same as double-clicking the file in Explorer.
To create an executable of your VI you need the Application Builder. It is distributed with the "Professional" edition of LabVIEW. For other editions you need to buy it. The computer where you intend to run your built application will require the LabVIEW Run-Time Engine, but that's free. You can choose to bundle it when you build the application, or provide it as a separate install.
As for doing this from another application, well that all depends on the other application. As I said, for Python, you need to check the Python documentation on how to call an executable.