Hi,
Probably the fastest way to get this up a running will be to convert your CVI application into a DLL. Instead of creating an EXE project you create a DLL project that exposes some functions that LabVIEW can call.
I am attaching a sample DLL project and the VI to call that DLL. The architecture there is very common where you create an initialize function, a function to perform an action and another one to retrieve the data. You can use this template to paste the current code from the executable and call it in LabVIEW.
Here is also a link to a document that has some more information on DLLs.
I hope this helps.
Regards,
Juan Carlos
N.I.