No.  But… Eating less meat and more fruit and vegetables is likely to help reduce stone formation.  Reducing the intake of meat, fish and cheese is thought to be beneficial, as it reduces the amount of cystine the kidneys have to handle. A plant based diet can also help alkaline the urine, which makes cystine more soluble and less likely to form stones.
Dr David Goldfarb answer:
Protein ingestion leads to more urinary acid to excrete. Fruits and vegetables lead to alkalization. This may be a more important reason to restrict protein intake than limiting methionine intake. I agree that the benefit of diet in the long run is not well studied, in children or adults and that protein intake could be overcome by more water drinking and effective alkalization. But I’ve noted that some of you out there claim to have benefited from a more vegetarian diet and I would bet that the effect on urine pH is more important than the effect on cystine excretion.