Sounds like a Vacuum leak in brake booster.
Apply the parking brake.
There are a couple of things that might cause a Chevy Tahoe to lurch forward after releasing the brake. One reason could be that the idle is high. The drive shaft may have to be greased.
You must apply your foot on the brake while shifting into drive.
Drive straight If puncture is in the front Tyre apply rear wheel brake That is hand brake. If the puncture is in rear tires apply the regular brakes.
Check your power steering fliud, if it is low this could cause the vibration you are feeling.
The 2007 Chevrolet Tahoe has rear wheel drive.
The 2008 Chevrolet Tahoe has rear wheel drive.
The 2006 Chevrolet Tahoe has rear wheel drive.
The 2005 Chevrolet Tahoe has rear wheel drive.
The 2015 Chevrolet Tahoe has rear wheel drive.
The 2011 Chevrolet Tahoe has rear wheel drive.
The 2001 Chevrolet Tahoe has rear wheel drive.