Does lockdown mode disable permanently deleting messages

Hello Douboyx,

I will start by saying this is a feature you should not enabled unless you're actively being targeted by a hacker/attacker. This feature isn't supposed to be used to "boost" your iPhone's security. There are a lot of other safer settings you can use to achieve this.

Lockdown Mode works by disabling a lot of features of iPhone to prevent an hacker/attacker from targeting your device, getting into your device, adding persistence, and accessing your data. The support page you came from lists everything Lockdown Mode does, but I'll list them again;

• Messages - Most message attachment types are blocked, other than certain images, video, and audio. Some features, such as links and link previews, are unavailable. 
• Web browsing - Certain complex web technologies are blocked, which might cause some websites to load more slowly or not operate correctly. In addition, web fonts might not be displayed, and images might be replaced with a missing image icon.
• FaceTime - Incoming FaceTime calls are blocked unless you have previously called that person or contact.
• Apple services - Incoming invitations for Apple services, such as invitations to manage a home in the Home app, are blocked unless you have previously invited that person.
• Shared Albums - Shared albums are removed from the Photos app, and new Shared Album invitations are blocked. You can still view these shared albums on other devices that don’t have Lockdown Mode enabled. When you turn off Lockdown Mode, you need to turn Shared Albums on again in your device settings.
• Device connections - To connect your iPhone or iPad to an accessory or another computer, the device needs to be unlocked. To connect your Mac laptop with Apple silicon to an accessory, your Mac needs to be unlocked and explicit approval provided.
• Configuration profiles - Configuration profiles can’t be installed, and the device can’t be enrolled in Mobile Device Management or device supervision while in Lockdown Mode.

You should still be able to delete text messages and iMessages while Lockdown Mode is enabled. The same goes for emails. However, please do not enable this feature unless you're actively being targeted by a hacker/attacker.