As SravanKrA writes, your iPhone cannot receive SMS messages if it is completely switched off.
But if you don't see your messages on the Lock screen when your screen is locked, check if the feature is enabled. Go to: Settings → Notifications → Messages
There must be ✓ in Lock Screen:
Also check if you have a Focus profile activated. For example Do Not Disturb. Do Not Disturb does not show notifications for messages and other apps when enabled. You can disable Do Not Disturb in the Control Center, and you can view and edit your Focus profiles here: Settings → Focus