So-called negative calorie foods are supposed to require more energy to digest than they provide. If one eats nothing but lettuce, yes, they will lose weight, possibly faster than if they starved themselves by eating nothing. Another aspect of negative calorie foods is their contribution of fiber, which is not digested, and which also blocks absorbtion of food calories by whatever part of the gut they're in contact with. Fiber also speeds the transport of food through the digestive tract, giving less time to absorb calories. I expect that a person who continued to eat exactly the same stuff, but topped each meal with a pound or two of celery or lettuce (without dressing or anything to actually make it yummy), would see noticable loss of weight. (And a pretty dramatic increase in their consumption of toilet paper).
However, the only true negative calorie food is ice. Eating ice provides zero calories of food energy, while requiring your body to burn energy to make up for the heat lost as it melts and warms the ice to body temperature. Awesome way to lose weight, no? But, (of course), it turns out it's not that simple. Every kilogram of ice you eat only requires 70 food calories to melt. You have to subtract 3500 food calories to lose a pound, so you'd need to eat over 110 pounds of ice for every pound of fat you want to lose.
