My Lirope is turning yellow and eventually dies.

Do you have voles or moles in your yard? They love to go under and eat the roots, then the lirope starts to die. If you do, try digging around the liriope and putting some crushed oyster shells in the little trench, then cover up with dirt.

https://www.gardeningknowhow.com/ornamental/groundcover/monkey-grass/monkey-grass-disease-crown-rot-causes-yellow-leaves.htm

Or maybe the victim of overwatering?

Is it under a downspout where it gets too much water? Could be a number of issues- this sounds similar to my hosta problem of root fungus as well, so you may have to pull it out , discard and treat the soil with an all purpose fungicide. Moles won't eat your plants but voles will. In this case a slow yellowing indicates a disease or water issue, imho. Hope this helps!