Clara - 'Rapped' does mean knocked, but 'smartly' doesn't mean lightly. If you do something 'smartly' it means quickly, firmly and confidently.

The sentences from 'Anne Green Gables' is: "Mrs. Rachel rapped smartly at the kitchen door...." and "Rachel Lynde rapped smartly on the front door, .....". And here, the phrase "Rapped Smartly the kitchen door" means: "To knock the kitchen door lightly" OR: "Lightly knock the kitchen door". Did it help you ?

Perhaps you should supply the whole sentence. I presume it means that someone was knocking on the door firmly with their knuckles/walking stick etc.