I try to keep it watered but it doesn't help. Since I have so many trees the bulk of my yard is shaded and the grass in these areas are slim, I get mold growing on the surface in-between the clumps of grass. In the areas that get a lot of sun it seems to die out and water grass comes in. I have been putting K-31 grass mix in the sun areas and creeping red Fescue in the shaded areas it looks good up till the dog days of summer. I also cut it tall to try and keep the weeds from coming up.
Clay soil needs organic matter and lots of it.
You may need to just cover the lawn with manure and straw for the whole winter. Your problem is clay soil, shade, tree roots and water. Scott is right. Organic matter is the answer to most of the problems. Well finished compost is the best for lawns as it quickly blends in and will disappear from view soon.