A. Ants are certainly a nuisance but they usually are easily dealt with by brushing out the anthills. However, you seem to have been taken over. It may be your lawn is a particularly attractive area for the queen(s) to have settled in. Regular scarifying, aerating and treating for moss and weeds will help create healthier grass and limit the invasion of new queens but your problem obviously needs a quicker fix. The problem is the nests cover much greater areas underground than is obvious on the surface. It’s worth trying, if you haven’t already, introducing a pathogenic nematode which will infect and kill the larvae and cause irritation to the adults so they abandon the nest and disperse. Nemasys No Ants is a product that contains nematodes that are harmless other than to the ants. It comes as a powder which is mixed with water and the microscopic, worm-like nematodes are watered into the soil where the ants are bringing it to the surface. Follow the instructions carefully as it is a cure rather than a preventative, so needs to be applied in the right conditions. Below is a link to the Royal Horticultural Society list of biological control suppliers which may also help you in your quest for a solution.
Royal Horticultural Society biological control suppliers