[MJN]

Originally Posted by hatzie

The 5.3L with AFM ( Yes the 2005-2006 LH6 5.3L had AFM ) has a filter screen under the oil pressure sensor that gets plugged up with crud. It makes the lifters clatter from starvation. Oil pressure to the crank is just fine but the lifters aren't getting fed. The LS4 in my Impala SS has the same filter and it's miserable to access on the transverse V8 engine.

The other thing the early LS engines had to contend with was the pressure relief valve in the oil pump getting dodgy.

Be it a stuffed screen, failing pickup tube O-ring, or failing pressure relief you need to address this ASAP.
In comparison to the oil pump and pickup the AFM filter screen is easy to access. Get a new GM oil pressure sensor along with the AFM filter screen and replace both of them.

If that doesn't fix your problem... You'll have to pull the timing cover and the oil pan to get to all of the bits and pieces of the oil pump. It's driven off the crankshaft snout.
Get a Melling pump and pickup kit. Stock replacement from Melling will work great. You don't need high volume or high pressure.
You may want to source a GM cam retaining plate ( these leak sometimes ) and timing chain/sprockets depending on your engine age.
I would also thoroughly and carefully evaluate the harmonic balancer, serpentine belt idlers & tensioners, and the water pump while you have em off.
Replacing the thermostat goes without saying. It's super cheap and you're there already. Stant or GM.

The OP has a 1500HD- it has a 6.0L not the 5.3L. AFM is not applicable on the 6.0L.
Curious why the OP hasn't responded or posted since- it would be good to get some more detail about whats happening.