Running a VI via a web server is explained in the LabVIEW documentation. No additional toolkits are required. However, the computer where the application will be running requires the Run-Time Engine, which gets installed when you install LabVIEW. If this is going to be on another computer you can install the Run-Time Engine either from the LabVIEW CDs, or you can download it for free, or you can bundle it when you build the application.
The easiest solution is to have the web server and the computer running the LabVIEW application be the same machine. It sounds like you can do this based on your post. So, set up the computer running the LabVIEW app as a web server in order to accept HTTP requests, configure the LabVIEW application's web server (again, see the LabVIEW documentation for full details), and you should be set. If the web server and the computer running the LabVIEW application are two different machines then you obviously need a mechanism to talk back and forth.