Open the Messages app
Open the conversation you want to lock
Tap the contact name or number at the top
Turn on Hide Alerts to mute notifications
Use Face ID, Touch ID, or passcode to lock your iPhone
Turn on Screen Time restrictions for Messages if needed
Go to Settings
Tap Screen Time
Tap App Limits or Communication Limits
Set restrictions for Messages access
Use Notes app with a locked note for private text you want to save
Copy the message into a locked note if you want to secure it