All diets work because they restrict calories. You cannot diet to get to a target weight, then resume your normal eating. Your weight is a reflection of the equilibrium between your eating habits and activity. Having a stable lower weight happens when we make a permanent shift.
Now, assuming you are interested in running performance, low-carb seems like a difficult way to go. But also, I don't think a vegan diet will work as a weight loss tool alone. It requires a lot of learning to figure out how to still eat well with so many foods off the table. People typically struggle to go vegan because they just cut out meat and don't add in enough other foods. Which accomplishes calorie restriction, but at the cost of missing nutrients.
There are easier shifts that aren't diets. Like resolving to eat less sugar and processed foods. If you shift the way you eat food (cooking at home more often, and good foods), that's a lifestyle shift that you can keep forever.