Answer: It sounds as though water is running off before having the opportunity to soak into the soil. This is usually a soil compaction problem. You may be able to counteract this by aerating your lawn. Rent an aerator at your local garden center and run it over your lawn. It will pull out plugs which you can leave on your lawn (they will decompose). Then spread some sand over the lawn. It will work its way down into the holes where the plugs were. The sand will allow the water to penetrate the soil, which should help your lawn green up.
Best wishes with your landscape!
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