When a text message is received, a tone is sounded and a short preview of the message or an Apple Intelligence message summary is displayed on the phone's lock screen; VoiceOver announces that you have a message and will probably speak it in full but if you have Apple Intelligence summarisation turned on you will only hear the summary. If you miss it first time, explore the lock screen with your finger by sliding your finger up from the bottom centre of the screen to locate the message; Lift your finger and it will be spoken. If the iPhone or iPad has already locked then click the side or top button to display the lock screen again and then explore the screen with your finger to locate the text message.
Occasionally your iPhone or iPad may lock while the message is being spoken and you won't hear the rest of the message. Try displaying the lock screen again and exploring again for the message. If that doesn't work double tap the message. This will open the Messages app and the full message will be spoken. This is also how you can hear the full message if the lock screen notification was summarised by Apple Intelligence.
If you want to reply to the message after you hear it spoken on the lock screen, slide your finger to locate the message and then double tap; the messages app will be opened and you'll be taken to a text field where you can enter a reply. If you dictate your reply, swipe right to locate the Send button and double tap. If you used the keyboard to enter your reply, locate the Send button a little above the top right corner of the on-screen keyboard, lift your finger and double tap to send your reply.
If the message no longer displays on the lock screen, you can use the Messages app where you can read and reply to all your messages. You can also delete messages that are no longer required in the Messages app. See all you need to know about messages with VoiceOver.
If you prefer not to have messages displayed and spoken on the lock screen one solution is to go to Settings / Notifications / Show Previews and change the setting to Never or When Unlocked. This sets the default behaviour for all apps. You can also turn off Apple Intelligence summarisation of all notifications lower down in Settings / Notifications. The preview shows a few lines of messages but VoiceOver generally speaks the entire message. If you turn off lock screen previews, you will still receive notifications informing you that you have received a message but the message itself will not be displayed or spoken. You can also turn off lock screen notifications completely for individual apps in Settings / Notifications using the list of apps in that setting.