Your normal weapon damage doesn't list surprise attack damage either. But I am making the assumption that there's extra damage with a surprised lunge since that may simply not be the case.
Regardless, there's still use for lunging through doors. Because of the fast movement of crabs, sometimes the only way to lunge at a crab is by backing out of the doorway and then lunging. It's also useful against projectile champions. By lunging through and then backing behind the door, you'll get a surprise attack in versus waiting for it to reach the doorway.
Yeah, I would use a levitation potion and wait until it ran out so I would fall directly down the well.
Something related I learned is plunging down without any aid on the first or second floor. The damage is minimal and you should be able to recover the loss easily in the beginning. Just make sure you have like 3/4 health. It's a bit riskier on the second floor because you could get unlucky with crabs or champions on the third floor, if you haven't healed up before exiting the room.