You should be able to edit SQLite outside of Pro. However, the compatibility between Pro and SQLite, SpatiaLite, and GeoPackage databases still seems a bit lacking to me. I've found that when such databases are created in Pro, they run into the same issues you're experiencing.
Use some other software to create the database first. There are a number of ways you might do it, but the GeoPackage Implementations page is a good start. (I know it's for GeoPackage, but GeoPackage kind of is SQLite, and many of the entries in this list support both.)
If you use an existing DB and simply interact with it in Pro, odds are you'll run into fewer issues.
- Josh Carlson
Kendall County GIS