Ants are excellent predators of many lawn and garden pests (plus termites), so if you can tolerate their presence, we suggest you leave them as-is. Their nest tunnels are also aerating the soil, which benefits root health. If discouraged from nesting in this location, the colony will simply "pack up and move" to another site, probably within the same yard (and hopefully not into the house). Two methods of discouraging them would involve digging into the nest site (which would damage or stress the turf roots) and trying to flood them out with a lot of watering, though this too risks drowning or stressing turf roots if done too often or extensively. (If the colony has been in this spot for a few years, the excessively-rainy years of 2018 and 2019 didn't seem to discourage them, so that may not work.)

Only the use of a insecticidal ant bait might eliminate the colony passively, though even aside from the unnecessary insecticide use, this is not likely to work well for outdoor ant colonies that have a wide range of resources they can rely on. Most ant bait stations are designed for indoor use only.

If parts of the lawn inhabited by the ants are struggling, it's likely due to other factors unrelated to the nest. (Too much shade, moisture/drainage issues, pH out of the ideal range, etc.) The ants chose a site suitable to excavation based on existing conditions and did not significantly alter the soil conditions to suit their needs; in other words, anything causing poor rooting or growth of the turf was pre-existing to the nest becoming this extensive.

Miri