What SMS app are you using?
Any SMS/MMS I get wakes the screen for me.
Make sure Settings > Sound & Notifications > Lock Screen is set to show all notifications. Make sure you haven't set the app-specific notifications to "None" for your SMS client (Settings > Sound & Notifications > Apps).
Lastly, check your SMS client (I use Chomp) to make sure notifications are enabled there. Chomp has a specific setting that says, "Screen Comes On" so that it will wake the screen when you receive an SMS.