Fresh lemons and limes last up to 10 days when stored properly. Do not store lemons and limes in plastic bags. The limited oxygen and the natural release of ethylene gas will cause them to spoil faster. Limes do seem to spoil more quickly than lemons, so be sure to refrigerate them right after buying them from the store or picking from the tree. Lemons can stay at room temperature for about 5 days, but will last up to 10 when refrigerated.
Lemons and limes will ripen by getting softer at home, but will never get jucier or sweeter after being picked from the tree.
In order to cut and store lemon and lime juice, be sure to remove from the refrigerator and let them come to room temperature. Roll the lemon or lime on the surface of a counter in between your hand or forearm to release juices and make the juice easier to extract. Slice and use, or cut in half and remove seeds and squeeze with a juicer or by hand. In order to store, squeeze fresh juice into ice cube trays and freeze. Store the frozen lemon, lime cubes in freezer storage bags sealed tightly until next use.