Solution
Why the error?
Building a stand-alone application with LabVIEW that includes GPU computing uses external libraries, but it only knows about those libraries called from CLNs (Call Library Function Nodes) where the library name (and possibly path) are hard-coded in the node. For the GPU toolkit to support multiple CUDA versions and different Windows platforms (i.e. 32- and 64-bit versions) from a single API, certain libraries are identified at run-time and passed to the CLN for execution. This is (a) how an lvcuda*.dll library is used in the LVCUDA API and (b) why they do not show up as a dependency like other external libraries (e.g. lvgpu32.dll or lvgpu64.dll).
The Fix
The GPU toolkit installs lvcuda*.dll in a lvgpu folder under LabVIEW's resource directory. This is part of the default path LabVIEW uses (in the development environment) to locate external binaries. No such default directory exists once you build a stand-alone application. However, there is still a search path used by the executable to find binaries it needs. The details regarding this can be found at
Executable Cannot Find My DLL Even With A Specified Path . Sometimes it's valuable to find out what dependencies these binaries have (e.g. a library which is itself linked to another library). The article
Determine What Calls Are Made by My DLL or Executable in LabWindows™/CVI™ discusses how to track such dependencies.
While these resources describe a few ways to make external libraries work from a stand-alone application, copying the external libraries to the system directory appears to be the most straightforward and yields success 100% of the time as long as the DLLs are put in the proper place.
For a 32-bit app, copy lvcuda32.dll to <windows_root>\system\lvgpu. For a 64-bit app, copy lvcuda64.dll to <windows_root>\System32\lvgpu. The 'lvgpu' subdirectory is required as this is the folder structure used inside LabVIEW's resource directory. Note that you do not have to do anything special with lvgpu32.dll or lvgpu64.dll. These libraries are recognized as dependencies and the VIs that call them will automatically look for them in their new location based on the build specification.
Alternatives
If copying files to the system directory is not an option, the executable can look for libraries using the PATH environment variable. Appending the library location to the PATH can have unintended consequences or encounter other problems (e.g. too many characters on 32-bit OSes) so it's not always a fail-safe or recommended approach.
Copying the libraries into the run-time engines folder may also work, but this is modifying a Program Files folder. Whether these changes persist during some installation modifications is undefined. In addition, you'd need to copy the libraries to each version of the run-time engine your application is built against.