Always prefer sealing the lemons in a zip-lock bag. Squeezing out as much air as you can. This will help the lemons retain their juice and flavour as long as four weeks.
If you have used one part of the lemon and wish to store the other, it is best to place the halved lemon on a small plate and wrap it a plastic wrap. Put it in an air-tight container and store it in the refrigerator.
If you have juiced the lemon and wish to store it, make sure you don't keep it at room temperature. Despite its acidic content, lemon juice has a tendency to promote bacteria growth if kept at room temperature. Avoid storing the juice in glass bottles as light will break down the juice more quickly. Rather, store it in a plastic container or glass container that is not transparent. It can last for about 2-3 days in the refrigerator.
One of the best ways to store lemon juice is to squeeze all the juice from the lemons in to an ice-tray and let it freeze. Now use them in any of your recipes without having to worry about their flavour or taste losing out.
A simple trick is to store them in a glass jar full of water. Add all the lemons you want to store and place them in the refrigerator.
Lemons are sensitive to ethylene, which is known as the ripening hormone that causes fruits to spoil. Therefore, never keep lemons near ethylene emitting fruits like apricots, apples, bananas, et al.
Make sure, the lemons you pick while buying should be thin-skinned as they are juicier than the ones with hard skin. If you are not buying lemons for immediate use, prefer buying green ones that take time to ripen.