Documenting inability to Start Editing SQLite geodatabase layers in ArcMap?
In the documentation, it is alluded to that you cannot edit data in a SQLite database from ArcMap:
You can connect from ArcGIS to an SQLite database to create maps and perform spatial analysis on your data.
However, the only place this appears to be explicitly stated by Esri is in the ArcGIS Discussion Forum:
Yes; you cannot edit data in a SQLite database from ArcMap.
It's not strictly read-only access. You can load data via copy/paste and import into a SQLite or SpatiaLite database. Tables and feature classes can be appended to using append or Load Data.
You can edit the SQLite/SpatiaLite data via code as Insert/Update/Delete are supported.
What you can't do is open an edit session in ArcMap.