I've seen some questions about the how and why lead works - here's an analogy to help you understand the vibration.
Sound IS a vibration of air molecules. The noise you hear is transferred from your engine or exhaust through the air to the cab of your truck. The energy carried in vibrating the air is transferred to the cab walls. Microscopically, that energy then vibrates the cab (it moves). That then moves the air inside the cab, hence you hear the noise. The more it vibrates, the more air is moved, the more your eardrum vibrates, and the louder it gets.
So - how do you eliminate it? If you can minimize the amount that your cab vibrates, then that transfers less energy into the air inside the cab. So the lead sheeting helps. How?
Well think of it this way. Lets say you weigh 200 pounds, and you and the 7 year old neighbor kid decide to swing on a swingset. Your wife applies a five pound force to you while you're sitting on the swing. You move, and swing back and forth maybe six inches. She applies the same force to the 40 pound kid, he swings back and forth maybe 12~15 inches. So the same energy applied to a weaker vibrating system (the 40 lb weight on a swing) results in more movement than is does a stronger system (the 200 lb man). So when you add a square foot of lead sheet to a square foot of sheet metal, you may be adding say 25~30% to the weight per square foot. The exterior sound level is the same, the same amount of energy is applied to your cab wall. But if it weighs more, then it moves less. This means that less vibration intensity is available to move the air inside the cab.
One other way to accomplish this is to stiffen the vibrating system. This is done by adding strength ribs to it. But this isn't practical in this application, or in this case probably not as effective.
The foam works because it disrupts the moving air, it acts like a cushion. The noise is still transferred, but it's confused (not direct) and therefore the intensity of it is reduced, it acts as a shock absorber. It also adds a small amount of mass to the system, and helps for reasons above.