Since CString is supposedly a container for constant strings, my guess is that your C++ project is Unicode and by attempting to cast CString to LPCSTR, you are also trying to convert wide string to ANSI.
(Without trying it myself first) try each of the following.
(1) drop the cast:
This will let the compiler decide what to do with strData instead of using your forced cast.
(2) if that doesn't work, change your project from Unicode to ANSI.
(3) if you can't do that, convert the wide character string to ANSI or else use the wide characters in the clipboard data. This is a little more complicated than can be easily shown here but is straightforward. Google will help you.
These items assume that strData is a CString (which you haven't properly shown).
Also, you should really get in the habit of using strcpy_s() instead of strcpy(). This is more modern and will help you fix dozens of bugs in your code.