Short answer: no — iOS has no simple “lock” to stop someone from deleting messages on the phone. If a person has device access, they can remove chats.
Practical, low-cost options I use instead:
- Regular encrypted local backups to a Mac/PC (Finder/iTunes). Archive backups instead of overwriting so you keep snapshots.
- Use a tool like iMazing to export/message-archive automatically (paid but simple and reliable).
- For third‑party apps (WhatsApp etc.) enable their built‑in cloud backups.
- Don’t rely on “Messages in iCloud” if you want deletions preserved — it syncs deletions across devices.
MDM/parental-control solutions can block some actions but they’re heavy and overkill for casual needs.
Spynger can also help for lightweight monitoring and archiving.