It's the AFM system that's the worst. The cam lobes and lifters can fail and send shavings through the motors which gets the pump sticking and wears the rings and oil consumption goes up. Another way they like to burn oil is from an AFM valve in the pan spraying oil on the bottom of the pistons and getting the rings gummed up. Another way is the early non-baffled valve covers pollute the intake and gum up the rings. I got mine with low mileage. At the first sign of valve train noise I'll get new cam and lifters with AFM delete to save the rest of the motor.
Would an 06 6.0 Denali have that? Not with the truck so I can't look at the VIN and build sheet. Truck ran good after it built pressure, and kept pressure up. Just the first start of the day, and 10 or 15 minutes of idling, is when it did this. Toward the end of our time driving it, it was getting a little worse about this. Quit driving it because the transmission temperature sensor was going out. Bought the new sensor; just never had time to tear into it, or $$ for transmission fluid.
And yes the lifters clatter when the pressure is low. I've heard many trucks, even several years newer,doing the same thing on startup. My 06 truck has 205 thou on it, so I guess it is an old LS thing