I understand that you hear an alert for incoming messages, but don't see a notification for them on your Lock Screen. I'm happy to provide some help for this issue.
Use the steps in the following article to ensure that notifications for Messages are allowed on the Lock Screen:
Use notifications on your iPhone, iPad, and iPod touch - Apple Support
Change alert styles and settings for notifications
Customize your notifications with different alert styles so you can quickly act on emails, calendar invites, messages, and more.
To add or change an alert style for a notification, go to Settings > Notifications and select an app. Here are some alert styles that you can choose:
- Allow Notifications: Turn on to get notifications from the app you selected.
- Sounds: Have an app play a sound to alert you when you receive a notification.
- Show on Lock Screen: Turn on to see notifications from the app on your Lock screen.
- Show in History: See previous notifications from the app you select.
- Banners: Choose how you want notifications to appear when your device is unlocked. Tap Temporary to have alerts appear on the screen and then go away. Or tap Persistent to have alerts stay on the screen until you act on it.
- Show Previews: Choose what you want to see when you get a notification, like a text message.
Thanks for using the Apple Support Communities. Cheers!