When can I go on a diet or lose weight after hair transplant?

It is best to ask your surgeon about post operative care as each doctor has their unique regimen.  Crash diets may be harmful to your body (as well as your hair).  

Going on a 500 calorie diet shouldn't affect your hair transplant grafts one month after the surgery. However, everyone is different, and every effect cannot be predicted. Possibly a less severe diet may be a better choice. You could still lose weight with a 1000 calorie low carbohydrate, and the risk of hair loss would be less. Not that you are an anorexic, but you should know that anorexics do lose hair, so it is a risk.Thank you for your question, and good luck.

Good question. Crash diets is a hair loss cause. So, I will suggest you to take it easy reducing weight  A balanced diet is always recommended. Also you can consult your primary care physician or dietitian too.
  

Be smart about dieting so that you don't lose hair. 500 calorie diet is not a smart diet so eat a healthy diet with reduced caloric intake