Dig it out. But it will fill back in.

This winter, cut back all the leaves to the ground. Just as new growth begins in spring, dig out the plants. Using a sharp shovel or knife, divide the plants around the new growth sections and replant as you wish. Depending on the type of liriope you have, it may grow fast or slowly to fill in. But you can keep it under control each spring by removing some of it.

I wish I lived close enough- I'd come and take some off of your hands! (I'm planning on planting some more liriope next year to replace scraggly creeping juniper). I was wondering what you meant by it looking terrible- has it taken over? I was just thinking that it may be easier to remove sections of it with a large shovel, and then add other plantings around it as you modify your landscaping. You could even dig it up, and divide it into clumps, and replant it the way you'd like. You could move it if you had use for it elsewhere in your garden. It's pretty rugged stuff. Thinning it out seems tedious, especially if it grows back quickly. But then, I don't know how large an area is covering your garden.

I'd guess it looks terrible because it hasn't been cut back in a while. In my experience, it looks best cut to the ground in late winter so it new growth is fully green and lush. Hopefully for you, its only a matter of you wanting it to look more presentable. If you really don't want it in certain areas, you've got a battle on your hands because of its aggressive root system. It'll take some thourough digging and selective herbicide treatments to keep it in check. You could also ask your friends, neighbors and coworkers or whoever if they'd like some -- for as much as the home improvement centers want for a small start of that stuff, most people should jump at the chance to get freebies. Lowes here where I live is charging $4+ for a one gallon container with a teeny tiny start of it poking out. If people only knew. Good luck with your pending project. You should take some before and after pictures so you can look back at the differences... =)