Yeah, this problem has been driving me nuts on and off for days.  The documentation that comes with the:
sqlite-dotnet-x86-1007300.exe and
sqlite-dotnet-x64-1007300.exe
installers states the following about distribution:

-- Quote --
Distributing the Binaries (Desktop)
System.Data.SQLite.DLL is a mixed assembly signed with a strong name in case you want to add it to the Global Assembly Cache (GAC). This is the only DLL required to be redistributed with your application(s).  It comes in 3 flavors: Win32, Itanium and x64 (AMD64).

Distributing the Binaries (Compact Framework)
System.Data.SQLite.DLL and SQLite.Interop.XXX.DLL must be deployed on the Compact Framework.  The XXX is the build number of the System.Data.SQLite library (e.g. "059").  SQLite.Interop.XXX is a fully native assembly compiled for the ARM processor, and System.Data.SQLite is the fully-managed Compact Framework assembly.
-- End Quote --

At a minimum, this should be updated to state the actual dependancies for distribution.  Note that for desktop it says that the System.Data.SQLite.DLL is all that's required. If not statically linked, msvcr100.dll and any others should also be included.  This would have saved me and all on this post grief.