So my friend gave me permission to drive his truck and he is with me through the entire drive time And I put a dent into the side of the door Could his parents sue me 4 not paying for the damages?

If you were driving someone else's truck and put a dent in the door, you are responsible to pay for the damages. They can sue you but you will also lose your friend. It's not worth it. Just take responsibility for what you did and do the right thing.