Even if you load the System.Data.SQLite.Core package from Nuget Package manager, the one click publishing installer doesn’t but the dlls in the correct sub folders.  So I didn the following steps, I created x64 and x86 folders in my project, then I added the SQLite.Interop.dll from each of the same directories in the default bin folder.  in the files in the publishing tab, I made sure these were copied and folders created in the installed app (as shown in the second picture.)

When I moved the project from GitHub to another computer, I had to use Nuget Manager to reinstall the packages.  (I didn’t have to go to the \packages\System.Data.SQLite.Core.1.0.112.1\build\net40\x64 and x86 folders and add add those back in to the project file.)