Now that your starts have graduated to a 3” pot, they can live happily (with sunlight and water) in their pots for months. The majority of the starts we transplanted into 3” pots at the end of June 2018 were planted out in their forever homes about 2 months later. However, since we had more plants than we needed, we saved approximately 30 of them in the greenhouse all winter, and used those starts to replace the unlucky few that didn’t survive the winter outside. Those 30 plants had been in 3” pots for 7 months by the time we planted them out, and seemed perfectly content.
That’s it! After another month or so－or end of July/beginning of August, assuming you took your cuttings in May－you’ll have several new lavender plants at a fraction of the cost of buying them at a nursery (and absolute certainty that they’re the variety you are looking for.) You can plant them out in August/September depending on your hardiness zone, or if you’re concerned about them surviving the winter, wait until next spring. So long as you’ve got a temperate, sunny spot for them to hang out in, they’ll be fine in their pots until you’re ready to plant them outside!