If you want to store lemon without using refrigerator keep them away from direct sunlight if possible use the whole lemons within a few days of purchase.

If you want to store lemon in refrigerator for longer duration keep them in a zip-locked bags, squeeze out as much air as possible then keep them in the middle shelves or door shelves of refrigerator.

For storing cut lemons cut-side down on a plastic wrap thoroughly wrap the lemons then put the lemons in an airtight container and safely keep in the refrigerator for at least 2 to 3 days.

To store lemon juice for longer duration, first pour lemon juice in a dark color bottle so that light can't easily pass through the bottle then keep it in the refrigerator for at least 2 to 3 days.

You can pour lemon juice in ice cube trays.  When lemon juice become frozen, transfer to a sealed plastic bag and keep in the freezer.After that you can easily use them to your dishes.

If you want to store zested lemon within 2 to 3 days , then transfer the freshly grated zest to an airtight glass container and store in a cool, dry location.