It's an age-old dilemma: beautiful lawn or dense shade. The two are incompatible. If you want a dense lawn, you may have to thin the trees to let in more light. Or you can plant shade-tolerant groundcover that will grow well in the shade. Many groundcovers tolerate some foot traffic and make a beautiful lawn substitute. Rather than planting the groundcover in a patchwork manner, make larger beds out of it. You may choose to get rid of the grass in the areas with deepest shade, but work at keeping the grass growing in the sunnier spots or where the grass is growing best.