We do sell an ant killer for lawns. http://www.bonide.com/products/insect-control/view/60613/ant-flea-and-tick-killer
However, the ants are probably not destroying the lawn. The ants may be doing so well because of an excellent food source in that area of lawn…grubs. The long term solution is to control the grubs in the lawn since they eat the roots off the grass. My favorite grub control is the only organic one Milky Spore. Here’s a link to more on your grub control options: https://blog.timesunion.com/gardening/you-should-treat-for-lawn-grubs-when-there-are-none/7204/