Ants do not feed on grasses and typically the only time ants are issues with grass growing is in very short mown grass because the blades will be dulled by the ant mounds.  Excessive mounding by ants can occur but rarely does this cause large patches of grass being killed such as in these pictures.  The pictures are very poor and do not show much other than an area that is bare of grass.  There is nothing in the pictures that suggests ants are responsible.  Since the ground is bare, ants will colonize it to their advantage.  I suggest determining if there was something else wrong that led to the grass dying (or send better pictures that show ants causing the damage).  Applications to remove ants from a lawn can cause a number of other problems to occur and may force surviving ants to move in high populations to surrounding properties.  There isn't anything that will keep ants from moving to new locations (insecticide-wise).  An ant bait could be applied, but it would take 6 - 8  weeks to work and other ant species will move into the area after the existing populations are removed.  I suspect the grass has either died or gone dormant from the drought and the ants have made the best of their opportunity, which could have finished off areas of weakened grass with the ant mounds they build.  Ants are highly beneficial to a turfgrass ecosystem and should be encouraged wherever and whenever possible.