Assuming you have a reference to SQLite.Interop.dll somewhere in your code, this is a problem that should be solvable with just the 'Copy referenced assemblies to workspace' setting.
Note that this setting only applies itself to the project you set it on, which in some cases isn't enough. If you are working with a reference sitting at the bottom of a dependency chain, the setting needs to be turned on for all projects in the chain. If in doubt, try turning it on for your entire solution (just select all the projects in the window). Depending on whether this works, you can then selectively turn off the setting for the projects that don't need it.
The 'Additional files to include' setting isn't intended to be used to help solve assembly referencing issues. In some cases you can rig up solutions using this setting, but there will be side effects involved and it will create a dependency on your foreground build. If you want to try and get away from using the 'Copy referenced assemblies to workspace', you'll probably need to revisit how the assembly is being loaded. Autofac may box you away from this, but sometimes you can work around the box by pre-loading the reference manually using Assembly.LoadFrom in combination with the methods on the
NCrunch Environment class which can obtain the workspace locations of dependencies during test run-time.
Depending on the behaviour of Autofac, it may also be enough to simply turn on the
Pre-load assembly references setting as this will force the SQLLite assembly to be in the application domain before Autofac tries to load it.