The lunar set is a special set that can only be attracted under the different moon phases! The moon phases have varying lengths with the new and full moon moths only being available for 24 hours while some of the other phases can last a week or more! Flowers are randomly given by Trevor in exchange for fireflies.
To check which moth you will get before attracting, go into the incubator and select a Lunar flower and it will show you along the top of the flower inventory e.g "100% chance of attracting _______" moth so you can see which moth you will get and can avoid double ups. The moths and their corresponding moon phase are listed below:
New Moon - Io Moth
Crescent Moon - Olive Crescent Moth
Half Moon - Pink Star Moth
Gibbous Moon - Spanish Moon Moth
Full Moon - Luna Moth