Hmm - I found the problem. I needed to build with ReleaseNativeOnly config, to get the SQLite.Interop.dll. The win32/x86 file is placed in sqlite-netFx-source-1.0.89.0\bin\2010\Win32\ReleaseNativeOnly.
To get the 64 bit version change platform for Interop project by select properties on the solution, and change platform to x64 - rebuild. The file is placed in sqlite-netFx-source-1.0.89.0\bin\2010\x64\ReleaseNativeOnly.
I copied them to my project folder in the x86 and x64 folders and it works.