To propagate Liriope, the most common method is by division, where you carefully dig up a healthy clump of the plant and separate it into smaller sections, each with its own root system, and then replant the divisions in a new location; best done in early spring or late fall when the plant is actively growing. 

Key steps for propagating Liriope by division:

Choose a healthy clump: Select a well-established Liriope plant that has formed a thick clump. 

Water thoroughly: Water the plant a day before dividing to make the roots easier to separate. 

Dig up the plant: Carefully dig around the base of the clump to loosen the soil and lift the entire plant. 

Cut the root ball: Using a sharp knife or spade, cut through the root ball, ensuring each division has a good root system and several shoots. 

Re-pot or replant: Plant the divided sections in new locations, making sure not to bury the crown of the plant too deep. 

Important points to remember:

Sterilize your tools: Always clean your cutting tools with a disinfectant to prevent disease spread. 

Timing: Early spring or late fall are the best times to divide Liriope. 

Spacing: When replanting divisions, space them appropriately to allow for future growth.