@Jason Sarno - It would have to do with a human being in the drivers seat. Because of the weight on that side, it rolls the body in that direction at launch due to physics that I could take forever to explain but to summarize - Newton's First Law. This causes the passenger side to lift first thus fall first. You wouldn't see the same result with equally weighted people in both the driver and passenger seats, I would expect the exact opposite of what you noticed to occur and the left touch first in a right-hand drive version with the driver being the sole occupant. This is just a very educated guess though so, I defer to anyone else that has more compelling/convincing data.
I'm not sure I agree with this, particularly about the truck lifting. Perhaps I don't follow what you mean, but 'lift' would imply that the truck is lifting off the ground like an airplane achieves lift with it's wings. I don't think that's really happening with a truck, and I don't think the right side, the lighter side, is leaving the ground sooner than the left side.
My guess, and it is just a guess, is that the left side is applying more force against gravity, and therefore, stays in the air longer as it has more force to overcome gravity. Force is mass* acceleration, right? If both sides of the truck have equal acceleration, but the left side has more mass, then the left side has more force. And since gravity is the same force on objects regardless of their mass, then force of gravity would mean that the right side would not travel as high on the left side (since less force is applied against gravity than the right) ... and therefore, the left side would land sooner.
I wouldn't be surprised if that's totally incorrect though. My brain tells me that if two separate vehicles with different weights approach the same jump with the same acceleration, the lighter vehicle would go higher and land later. But, this is one of those things where your instinct isn't always right. I think the reality is that the lighter vehicle is likely to approach the jump with greater acceleration, and thus apply the same or more force than the heavier vehicle would. All I know for sure is that a heavier object doesn't fall faster than a lighter object, so the reason one side falls sooner than the other has to be on the rising part of the jump, rather than the falling.