I left my iPhone in a taxi cab. I locked the phone to make sure nobody finds it and makes expensive calls. But does locking the phone prevent someone from seeing the texts I am sending? What if the battery dies? After the phone is recharged, will the texts I send still be readable if the phone is locked?
Your sending a lock doesn't change the settings you had on the phone prior to losing it.
If messages were showing on the screen - they will still show.
If not, they will not.
If you have find my phone enabled and are concerned about changing this, you could send a remote erase (and then lose all ability to track it again) and have it resort to the default behavior. I'm hesitant to erase my phone now to test, but am fairly certain the default is towards privacy and further messages would not be displayed on the lock screen when the phone reboots or is powered on again.
If you locked the phone through iCloud / MobileMe it will appear the same as if you enabled the lock on the device itself, plus it will lock immediately (as soon as the action is done) and you'll receive an email notification telling you that it is done. The iPhone will remain locked after it has been shutdown or lost all its charge. So, in theory, it shouldn't give up your messages.
They may not be able to log onto AT&T or unlock your phone to read your texts. However, if they have access to your iPhone, they can listen to your texts! Even under Settings → Notifications with the Show on Lock Screen option off, all someone has to do is ask Siri to read messages and she will! So turn off Siri to keep those text private!