By the looks of it your problem really isn't being caused by the tree. It may be having some effect but it doesn't look like it's the major part of your problem. You actually seem to have more grass near the tree than you do away from it. You don't state where you live in your thread or your header but more than likely it's too late in the season to recede your front lawn.
Your best bet is to probably take a soil sample and have your local nursery or agricultural extension service test it. You may need to add lines or some other materials to fortify the soil. You could do that now and let it normalize and be ready for fall seeding.
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