can i dye my grass

As grass grows quickly the dye would soon wear off, or like hair, you'd see the roots!
Not sure if you are serious with this question, but to get a better lawn just cut it more regularly (but not during drought periods) as one type of grass will predominate and you'll lose the patchiness. If the patchiness is caused by poor growth, use a lawn feed/fertiliser.

the short answer: no.

If it,s for a one off, you can. say for a garden party or something.
In our driving range (golf) The greenkeeper uses a dye on the grass for open days. not sure what it,s called though.
it doesn't harm the grass but doesn't last long and can make the lawn look worse if not applied properly