Usually Liriope foliage that gets worn-down over the winter like this (which is typical) is pruned off in March, so the cuts avoid damaging any emerging new growth in the crown (center) of the plant. Now, you can still try to prune it back, but will have to be more careful to avoid cutting the young foliage that might be emerging between the old leaves. It won't kill the plants if you do accidentally cut some of them in the process, but it may stunt growth for a time or give the plant a ragged look as those cut ends dry out and turn brown. Eventually the new growth will cover-up most of the old foliage (or stubble, if cut), so their look will improve in a month or so even if you don't take any action.

Liriope can be an aggressive plant, so thinning it would simply involve digging out clumps to relocate (or compost), as the plants should recover from the root disturbance well. Some types (Liriope muscari varieties) are clumping (though with close spacing they can grow into a carpet), while other types (Liriope spicata varieties) are true spreaders that behave more invasively. We can't tell from the photos which type you have, but based on its density, we'd guess the latter.

Thinning these plants isn't necessary (after all, Liriope spicata is used as a groundcover with the goal of creating a grassy-looking carpet), though reducing crowding can sometimes help to suppress certain disease outbreaks. Liriope of both types tends to grow and look its best in semi-shade (this exposure looks like more sun, but it's hard to tell), so sun stress might be a contributing factor to any bleached-looking foliage.

Miri

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