1. Enable the secure_delete pragma <https://antonz.org/sqlite-secure-delete/> so that when your user deletes something, the data is actually erased. Otherwise, when a user shares one of your application's files with someone else, the recipient could recover information that the sender thought they had deleted.
2. Enable the options described at <https://www.sqlite.org/security.html#untrusted_sqlite_databa...> under "Untrusted SQLite Database Files" to make it safer to open files from untrusted sources. No one wants to get pwned when they open an email attachment.
3. Be aware that when it comes to handling security vulnerabilities, the SQLite developers consider this use case to be niche ("few real-world applications" open SQLite database files from untrusted sources, they say) and they seem to get annoyed that people run fuzzers against SQLite, even though application file formats should definitely be fuzzed. https://www.sqlite.org/cves.html
They fail to mention any of this on their marketing pages about how you should use SQLite as an application file format.