Does lifting light weights with many repetitions do that?
Using more energy than you eat will do that. On my last major diet I went down to 7% bodyfat lifting in the 4-8 rep range, mainly 5x5, with no cardio. It was too hard on my body, I wasn't sleeping enough either, and I eventually blew a shoulder on the last exercise, of my last workout. It was an experiment to make sure my style/diets etc work that I give people.
8-12 reps is a good range on a diet to stay strong, and work hard. Often you can/will do more reps on legs. With squats you can get a lot out of 10-20 rep sets. 20 reps, with a weight you can really only do 13 with, the last 7 are just pure guts.
High protein, moderate fat (good fats), low carb. Really high protein.
Lifting light weights for high reps is essentially cardio so it will help in that it burns energy.
Good old dieting is the best way to lose fat but if you don't want to lose muscle while your at it then lift heavy weights as it gives your body an incentive to keep the muscle.
If you get your diet (what you eat AND when you eat) and your workouts sorted you can gain muscle while losing fat. It won't be the same as if you were eating heaps but it is possible.
Um, light weights is cardio? No, no it's not. Deiting is good, but you need to train well at the same time.
Losing fat and gaining muscle is the holy grail. If you have never trained hard and eaten well before, you can pull it off. If you have been training for a while and eating well, good luck without drugs, unless you are really out of shape....which you wouldn't be if you had been training hard and eating well for a while.