Rough idle

It is in the air intake duct right by air filter. It is a four wire connection, but make sure the duct work is connected and no holes in hoses or grommets on engine. Clean throttle plate on both sides with choke cleaner.

Http://www.2carpros.com/articles/engine-stalls-idles-too-high-low-after-dead-or-replaced-battery

I have also seen with some computerized vehicles, that getting on a lightly traveled road and getting your vehicle up to 60 mph or so, then letting go of all of the pedals and letting it coast down to basically nothingness will aid in the idle relearn process.

The medic

Misfires can be caused by worn or fouled spark plugs, a weak spark (weak coil, bad spark plug wire), loss of compression, vacuum leaks, anything that causes an unusually lean fuel mixture (lean misfire), an EGR valve that is stuck open, dirty fuel injectors, low fuel pressure, or even bad fuel.

Check the crankshaft sensor, its the one that detects missfires.

Information on Engine Misfire MIL/SES Light Illuminated or Flashing DTC P0300, P030...
Information on Engine Misfire MIL/SES Light Illuminated or Flashing DTC P0300, P0301, P0302, P0303, P0304, P0305, P0306, P0307, P0308, P0420 or P0430 TECHNICAL SERVICE BULLETIN Reference Number(s): 06-06-04-046, Â Date of Issue: Â September 12, 2006 1999-2007 Cadillac, Chevrolet, GMC Full-Size Pickup and/or Utility Trucks; with Affected 4.8L, 5.3L, 5.7L, 6.0L or 6.2L VORTEC GEN III, GEN IV, V-8 Engine (VINs V, C, Model(s): T, Z, B, 3, M, 0, J, R, U, N, Y, K, 8 - RPOs LR4, LY2, LM7, L59, L33, LC9, LH6, LMG, LY5, L31, LQ4, LQ9, L76, LY6, L92); with Active Fuel Management(tm) and E85 Flex Fuel Related Ref Number(s): 06-06-04-046
ARTICLE BEGINNING
SERVICE INFORMATION
The wire terminal (G103) attaches either to the front or to the rear of the right side cylinder head, depending on the model year of the Full Size Pickup and/or Utility Trucks. If the ECM ground terminal has been found to be corroded, then follow the service procedure outlined in this bulletin to correct the corrosion issue.
Fig. 1: Engine Wiring Harness Ground Terminal Location (2007 Full-Size Pickup and/or Utility Trucks)

Fig. 2: Engine Wiring Harness Ground Terminal Location (1999-2006 Full Size Pickup and/or Utility Trucks)

1. Remove either the nut or bolt securing the main engine wiring harness ground terminal (G103) to the right cylinder head. Refer to the above illustration to determine where the ground is located on the vehicle (1). 2. Remove all rust from the ground terminal, the cylinder head and the retaining nut or bolt. 3. Position the main engine wiring harness ground terminal and install the nut or bolt.
Tighten:: Tighten the retaining nut or bolt to 16 N.m (12 lb ft).
4. Apply some type of electrical moisture sealant to protect the harness terminal from further corrosion.

You should check the freeze frame data and check whether a code p0014 has set as well. This could also be a cam phaser stuck or failed that has caused this. I would think that would be more likely then chain stretch.

I do not think so. It could be chain stretch but they have tension-er's on them to keep stretch to a minimum and I have seen a lot of these go many miles before having this issue. If it is sludge you could always try choke cleaner to clean it off and free it up maybe. But as you said in the initial post this was run low on oil for a while so I guess your next move is go over everything and pull the cover. I am sure you will find something from doing that.

Hi You replaced the ECT which sends engine temp to PCM. The P0128 is thermostat not closing for engine to reach op. Temp. That would cause rough idle. The P01345 does cause concern but first replace thermo. And clear codes see what happens.
Thanks for donate