Liriope can get rather ragged looking. You can mow it back to a few inches high and it will return with fresh new growth. However if the plants are getting too much sun the new growth will only get burned looking again.
There is not a substitute that looks like liriope for bright sun areas. However you may find a dwarf yaupon shrub to be a good choice or perhaps a short statured clumping grass like Gulf Muhly.
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