What I learned years ago plowing snow was that a pickup truck, LS or not, is way too light in the rear.  When  expecting snow I would load the rear of mine with something (a pallet of concrete), or even just load it down with snow for traction.

Was the rear end faulty?  If you were on mostly ice, maybe not.  The problem with ice is that if there is more traction on one wheel than the other and you hammer it you can exceed the breakaway torque of the LS and it "thinks" you are turning, so only one tire spins.  This is why no serious off roader runs an LS: they are too unpredictable and will let you down when needed the most.  In that environment a locker is a much better choice, selectable or otherwise.  I know some guys that run mud bogs that run spools or welded rears. 

Now, on the street I find in a car an LS is usually less objectionable than a locker, which tend to clunk and bang.  I will say that the Traction Lock in the 8.8 was never a really great design.  They had too little surface area IMO.  They would wear out prematurely, or slip when you put real power in front of them.  If someone was dead set on a LS I would advise them to get a Yukon.  Much better than stock.  However, IMO a True Trac is an excellent choice for the street.  Nothing to wear out and they take plenty of power without complaint. 
 

I ordered the truck and it was supposed to come with a 3.55 LS.  It said it had one on the window sticker.  I don't think that I was ever under the truck to look at the tag on the rearend.   I just know that I was disappointed that both wheels wouldn't pull going up the driveway.
Yes when it snowed I always hoped that it would snow enough so that I could fill up the box with snow to put some weight over the wheels.  I've been driving a pickup since the 90's so I know all about the weight in the box.  That's the only way I could get up the driveway, and even then I occasionally had to leave it at the bottom of the hill and walk up to the house.  Used to tick me off when I couldn't get up the hill and my wife's front wheel drive car would cruise right up.

Try holding your foot on the brake to preload both wheels. Some traction lock rear ends require a more even load applied to both aides to lock

RV6 wrote:

MS wrote:

Try holding your foot on the brake to preload both wheels. Some traction lock rear ends require a more even load applied to both aides to lock

This does work. If'n you have a manual like me then application of the parking brake helps when the left foot is working the clutch. This also helps with OPEN differentials.
 

I've seen guys off road with the ability to apply the parking brake to one side or the other (two levers) as an el cheapo way to get better traction.