I wouldn't make any major dietary changes at least until supply is well established. Protein is one of the most important nutrients while breastfeeding and that's a big adjustment to make sure you're getting enough without meat. Breastfeeding also requires a higher caloric load overall, so it's going to be difficult to diet. You'll be craving carbs and need to snack frequently. If it's for weight loss, you're better off focusing on exercising imo.
My baby is only 3 weeks but I have noticed when I eat healthier more nutritious meals my supply is better than days that I don’t. It’s definitely better for baby and supply but just make sure you have ample protein and balanced vitamins if you go vegetarian.
I’m vegetarian and a week postpartum I have a good milk supply but I agree to not make major dietary changes and really focus on your protein intake if you do
I’ve been vegan for over 10 years and never had issues breastfeeding my kids.
Honestly I’ve just been drinking a peanut butter banana oatmeal smoothie everyday, and if it’s for breakfast I just put coffee in it. My milk supply has been on average 10 oz a day and my baby is less than 2 weeks old; but I’ve been pumping since before she came; also my milk supply has been increasing since she was born