A vegan low carb diet I believe may exhibit a bifurcation, 2 possibilities:

• Liberal soy proteins: soy milk, soy yogurt, tofu and all the gamut of soy products and TVP. Proteins would be no big prob. Plus all non starchy vegetables, nuts, seeds, olive oil, konjac and psyllium bread and all these lowcarb options. A bit boring maybe. The availability of soy proteins would also entail significant exposure to isoflavones. A real vegan could not care less though.
• Soy proteins no more than 15 grams per day. safe threshold for isoflavones. I would choose this option. Also, TVP sounds something so artificial and unhealthy that I'd rather eat meat. On top of that, I would need 35 more grams of proteins per day. A bit of a challenge. 100 grams of almonds = 18 g/proteins. 1 avocado = 10 grams of proteins. 250 grams of vegetables= 7 grams of proteins. I reached 50. Plus Coconut fat, 92% chocolate.... I wonder if I'd be able to follow such a diet. I doubt it. A reasond, scientific schedule of supplementation would probably be needed.