I low carb at the moment but my diet is def not vegan-friendly!
Following with interest as i'd like to cut down on my meat and dairy consumption
Initial thoughts are there are nuts, vegetables like cabbage, broccoli etc, oils like coconut oil or ghee (don't know if this is animal or not)
You could roast veggies in plenty of oil, eat plenty of nuts and seeds by check they are low carb friendly first.
Make sure you have a multivitamin and plenty of electrolytes too as it will be restrictive!