I've never read about bad lifters being a common issue on these 7.3s. If it clears up when warm I'd guess you either have a bad glow plug or a tired injector. Ohm out the GPs (look up the 50 cent mod for directions) and replace the bad one. Autolites have a bad rep.
If the GPs ohm out ok determine which side the sound comes from. Use a mechanics stethescope (or a long screwdriver or socket extension placed on the bone behind your ear) and touch it down to find the loudest spot. Keep it well clear of the belt and fan, obviously. Take off the valve cover and watch to see which injector is not spurting oil like the others when cold. That's the lazy one and it's just worn out. Below is a good read on injectors.
I might be way off base. Any other symptoms you can give us?