Thanks for sharing these extra details. I've built a sample project containing these references and have analysed the build logic involved here. It looks like the file is being copied via standard MSBuild logic. It's a bit more complicated than other references because this particular file seems to be platform/CPU specific, so it's kind of chained in to the system rather than specified directly. However, I don't seem to be seeing the same behaviour as you are. When NCrunch builds the project in its workspace, it seems to be copying the e_sqlite3.dll to the correct location.
When referencing the project from another project without the SQLLite dependency, e_sqlite3.dll is not copied into the referencing project's output directory (as designed), when 'Copy Referenced Assemblies to Workspace' is enabled, this file is also copied to the referencing project.
You mention that you're using this with a grid node. Are you noticing any difference in behaviour between the grid node and your local machine?
I just thought I'd also confirm that you're using NCrunch v3.12 (the latest build), since there's been quite a bit of work done on the CPS based projects over the last few months.