During a simulated soft field take off from a paved runway the student pilot followed the procedure of holding control wheel back pressure while accelerating for takeoff. The airplane began to lift off the runway into ground effect with an excessive nose high attitude and began drifting to left of center line. Upon realizing the airplane was in an imminent stall due to the high angle attack and veering away from the runway centerline, the flight instructor took over control of the airplane, but the airplane had already drifted over the grassy area off the left side of the runway. During the subsequent runway excursion, the right side of the horizontal stabilator struck two of the runway edge lights and incurred substantial damage. Neither the flight instructor, nor the student pilot, heard the impact and continued their flight lesson. The damage was discovered after they completed the lesson. Following the accident, the flight instructor stated that he should have been more proactive in either taking control, or ensuring the student was relaxing the back pressure on the control wheel as they started gaining speed to help get the airplane in to ground effect for the simulated soft field departure.