The place to start is with the soil. What did a good, reliable soil test tell you about your soil?
What is the level of organic matter in your soil"
What is the soils drainage ability?
What is the soils workability?
What is the life in your soil?
What does that soil smell like?

It is the beginning of anthracnose (Colletotrichum sp.), a pretty common fungal problem with liriope, especially if in very humid or over-watered conditions. Avoid late day watering and provide only enough irrigation to keep the plants happy......an automatic system with daily watering is more conducive to the development and spread of this problem than a much less frequent but deeper watering. Too much water/poor drainage can also lead to crown rot or Phytophthora. For established plantings of liriope, you can simply mow the liriope back, but I wouldn't suggest that drastic a measure for new plantings. Cut off the worst of the foliage.

Neem oil applications are recommended for many plant diseases, and this is one of them.

Sorry I'm so late in commenting. (I had stopped checking out the forum since there were no replies for two days.)

I've had plenty of trouble in my year and a half new yard with fungus so I'm not surprised. The landscapers put in some liriope 'evergreen giant' in the landscape but that came down with Phytophthora within a month. I was then told that liriope 'big blue' was not susceptible to fungal diseases so they were the replacements.

gardengal48 - I'm glad you mentioned anthracnose. I was just about to buy a dogwood tree for the back yard and I learned that they are susceptible to that. (So, nix that tree! and move on to something else.)

Thanks all.

Is there a moisture problem with the yard? Perhaps too much irrigation, etc?

As is the case with a number of fungal problems, there are many different types of anthracnose and they tend to be extremely plant-specific. So anthracnose that affects liriope (Colletotrichum sp.) is not the same strain of anthracnose that affects certain species of dogwoods (Discula sp.). Therefore, your decision in choosing a dogwood should not be determined by having a problem with your liriope :-) There are a number of wonderful dogwoods that are very resistant to anthracnose - any of the kousas, all the Rutgers hybrids, 'Eddie's White Wonder' and a recently developed cultivar of the very popular Eastern dogwood, Cornus florida 'Appalachian Spring'. You should have no problems with any of these.

I'd also agree with Rhizo and wonder at the reasons behind the development of a lot of fungal problems. Generally that would indicate a situation that had poorly draining soil combined with excess or improper irrigation practices. Or it could be something as simple as the wrong plant for that particular spot. It's worth examining a bit more closely to see if some simple adjustments can be made that would relieve the problem.