Immediately after removing the cutting from the mature plant, store them in moist growing material in order to protect the open cut area. Store them in a shady outside location until ready for planting. Once your stored cuttings begin to establish roots that are about 1” long, transplant them to traditional pots with potting soil.
Young cuttings need more water than mature plants, but it can be a delicate balance. If you begin to see blacked leaves at the base of the plant you need to cut back on the amount of water than your new lavender plants are getting.
Finally, once your new lavender plants have an establish root system that binds the potting soil together in the small pot, do the final transplant into their permanent home in your landscape.