You shouldn't include the SQLite project files with your project. The SQLite project has several dependencies and custom build steps that you are missing. The reason you're getting this error is because the System.Data.SQLite-Full project is an "intermediate project" which builds ONLY the wrapper. The "SQLite.Interop" project is responsible for compiling the native engine and merges it with the wrapper in a custom build step.
By referencing only the SQLite project, you're only getting the wrapper and the native engine isn't being merged with the assembly.
Robert