Liriope of all types can be cut back in mid to late winter, just prior to the onset of new growth which is usually in late winter or early spring. Then new growth comes in and fills in giving the plants a fresh new look. If the plants are getting too large and flopping over consider limiting water and fertilizer as this may help a little. The giant liriope really doesn't need fertilizing anyway and in your climate rainfall takes care of the watering needs in most seasons.
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