It's hard to identify holes in lawn soil from the signs of digging alone, but it could be ground-nesting bees (not wasps). A wide variety of our native bees are solitary ground-nesters (one example being the mining bee group), and while each female works on her own nest tunnel by herself, a grouping of them could inhabit a given area if the soil is suitable for their needs. (Readily-accessible in thinning turf, and easy to dig.)

While such insects can take advantage of declining turf, they are not responsible for its state of health (if anything, their digging probably improves aeration for the health of roots), and if you wanted to improve the lawn's condition (which may discourage the bees from reusing the site in future years), you can take the various steps discussed in our lawn care and maintenance pages to improve its vigor. (For example, depending on the lawn type you have, overseeding in autumn, dethatching, applying fertilizer and/or lime according to soil test results, using recommended turfgrass cultivars, core-aerating just prior to seeding, and so on.)

Some earthworms also produce castings (waste) that looks a bit like this, as might other soil-dwelling insects. We can say that there isn't a significant lawn pest that generates this type of soil mounds or pellets on the surface.

Miri