Difficult one - you need to uncover the main roots in the lawn, drill into them with a medium wood bit to make holes about quarter inch deep, then fill those holes with neat SBK without spilling it on anything else, cover with something (polythene, broken slabs, whatever). This will kill the whole root and should stop the problem, but it means you've got to find the major roots first and make plenty of holes - that probably means wrecking your lawn. I'd do it either immediately, hoping to repair the lawn in late September early October by reseeding or replacing turf in damaged areas over the top of the treatment, or wait till end of September to do it and leave it as it is till spring, when seeding can be done again.