If you're not planning to use fresh lemon zest straight away, the good news is that the peel keeps well in the refrigerator for around a week if stored in an airtight container.
However, your best bet would be still to freeze the zest. If you keep it in a resealable bag or an airtight container, lemon zest can last for up to a year in the freezer.
The best bit is that you don't need to defrost frozen zest. If a recipe calls for zest and you don't have any lemons handy, the zest in your freezer is all you need to reach for.