The badge isn't a totally reliable way to tell. I know a guy with an 06 lly with 6 speed and his just says "Duramax Diesel" like older ones
sent from a galaxy far far away
Badge on an 06LLY should still be the old style. LBZ got the new style.
As mentioned tapshifter is an indicator.
If the 8th VIN digit is a "2" and the `10th digit is a "6" then it is an 06LLY.
Pop the hood and if you do not see an FICM on the passenger side valvecover, its an LBZ. Also look at the turbo intake horn, LBZ's are much larger than LLY's. The cold side intercooler pipe will also give some indication as well. LLYs come up more towards the fender on that side of the air intake whereas LBZs come from the front more on that side of the air intake. There is also the 4 bolt flange where the intake grid heater is on the LBZ's. LLYs do not have this. The engine fan shroud should also be a giveaway. LLYs do not have the annoying supports everywhere whereas the LBZ's do.
NOTE: In the above paragraph LLY means 04.5-05LLY and LBZ means 06LLY-07LBZ.
That should be plenty to get you in the right direction.