I want to cut obscenities into my neighbor's lawn.
Why do that to their lawn?
I want them to see it and be surprised.
That is not something a good neighbor would do, in fact, it is vandalism. You should respect the property of your neighbors and leave their lawn alone.
I'm the one who has been complaining about their dog peeing on my lawn, I have a right to get back at them.
I can understand your frustration at your neighbor not cleaning up after their dog. However, while what they are doing is neglectful, what you propose to do is completely illegal. You should not try to get revenge on your neighbors, because you will just be inviting legal trouble for yourself.