Lavender reaches clean laundry through four main routes: detergent formulated with lavender oil or fragrance, rinse-stage softeners, dryer-stage products such as sheets and wool-ball drops, and storage-stage sachets or linen sprays. The later in the cycle the scent is added, the longer it tends to survive.
For home use, the reliable methods are simple: a few drops of oil on a wool dryer ball, or a dried-lavender sachet kept with folded clothes and refreshed every few weeks. Undiluted oil should never touch fabric directly, since it can stain and its concentration far exceeds anything a detergent delivers.