How to store
Store Amalfi lemons if possible not in a fridge but on a fruit bowl. Here you can preserve them for 1 or 2 weeks.
How to eat
Use the lemons as how you would use a normal lemon. For example, make jam, custard or lemon curd. The peel can be grated and used as a finishing touch in pasta or risottos. But the most excellent practice is of course to make limoncello from the peel!