In principle, people can eat grass; it is non-toxic and edible. As a practical food source, however, your lawn leaves a lot to be desired.
There are two main problems with a grass diet. The first is that human stomachs have difficulty digesting raw leaves and grasses. Animals such as cows, on the other hand, have a specialized stomach with four chambers to aid in the digestion of grass (a process called rumination).
Aside from the digestion issues, a second problem with grass as a food source is the mastication. Your dentist would not be pleased; grass contains a lot of silica, an abrasive which quickly wears down teeth. Grazing animals have teeth that are adapted to continually grow, replacing the worn tooth surfaces quickly.