NO, You can't refrigerate all the lemons for more days .
Lemons are still best within 2–3 days of cutting.
Despite its acidity, lemon juice can harbor bacteria if kept at room temperature. After about 2–4 days in the refrigerator, the juice will start to lose its taste. Throw it out once it looks dull and dark or loses most of its taste, usually about 7–10 days.
Do not store lemon juice in transparent bottles, since light will break down the juice more quickly.
Store-bought bottled lemon juice typically contains preservatives, which increase its shelf life to several months.