Soak the Liriope muscari berries for 24 hours in a vacuum flask full of warm water. Put on gloves. Remove the berries from the water. Squeeze the berries between your fingers to expel the seeds through the softened flesh. Rinse the seeds well.
Fill a nursery tray with a soil mixture comprised of 3 parts loam, 2 parts compost and 1 part perlite. Fill the nursery tray to within 1/4 inch of the brim. Saturate the top inch of soil using a water-filled spray bottle.
Sow the Liriope muscari seeds an inch apart in the nursery tray. Sow them at a depth of 1/2 inch. Sprinkle medium-grit sand across the surface of the soil mixture to help regulate the soil moisture during germination.
Place the nursery tray inside a greenhouse or indoors near a large, sunny window. Set the nursery tray atop a propagation mat. Adjust the temperature on the propagation mat to 68 F.
Moisten the soil with the water-filled spray bottle whenever it feels dry below the surface. Aim for making the soil lightly to moderately moist at all times, but try to keep it from becoming soggy.
Watch for the first signs of germination in 30 days. Transplant the individual Liriope muscari plants into 4-inch plastic pots once they reach 2 inches in height. Pot the seedlings in the soil mixture created in Step 2.
Place the individually potted Liriope muscari plants in a sunny spot while they grow and establish a productive root system. Keep the soil moderately moist, but let the surface dry out slightly between waterings.
Transplant the Liriope muscari plants 6 to 12 inches apart in a partially shaded bed two weeks after the last winter frost. Avoid planting them in full sun since the leaves will become bleached and wilted during hot weather.