You can diet, you can calorie count, you can exercise and you can lose weight while breastfeeding.
The caution is to not overdo the exercise, or lower your calorie count too drastically very quickly or you may see a drop in your supply.
The best recommendation is watch fat and calorie laden snack foods, choose healthier meals, and begin a walking or swimming routine because they are fairly easy on post pregnancy bodies. remember all of your joints are still loose from the hormones to loosen things up so your hips would spread for pregnancy and labor--so you may be at higher risk for some joint injuries if you go nutso. Don't drop calories by more than about 100 a day, stay at that level for a week or two while monitoring your supply before making another change.
realize that a lot of women do hold on to 10-20 lbs while breastfeeding. part of that is your body's protective effect on a bit of fat stores to ensure baby's milk always has the proper amount of fat and calories. But also, if you were to weigh your boobs when breastfeeding, they probably weigh 10 lbs when full of milk. if you weigh yourself first thing in the am when engorged, yeah well the scale might not look so nice. You have extra milk glands, ductwork, and milk storage which will account for some weight as long as you are still breastfeeding.