Hmmm, If I were going to be a strict vegetarian in fat adapted ketosis I would get SNP tested to make sure I have the right genetic polymorphisms to exclusively tolerate plant phytosterols (raw unsaturated fats) better than saturated fats and eat chlorella* (better than meat) for B-12 and an endless list of other micronutrients (vitamins, minerals, trace elements).
But if I was not one those peeps then I would probably fail (cardiovascular disease or a hyper- responder in reverse?) at being a strict vegetarian!
*Footnote: Chlorella and Spirulina contain both the animal (DHA/EPA) and plant based (ALA) omega3 fatty acids.