Dogs do this instinctively when they feel nauseous to induce vomiting, but it doesn’t always work. There may be some stomach issues going on, or it could just be a nasty habit that they have developed.
The only 2 dogs that I have owned that ate grass was one that had Lyme disease and kidney damage. The other one was a very healthy dog until she was diagnosed with hemangiosarcoma as a mature adult. Many lawns are treated with pesticides, so I would discourage them.
I would take them to the vet to rule out medical problems before you assume it is related to their diet.
