Well, I'm no expert but I will share with you what knowledge I hold:
I will not say it is impossible to lose 50lbs in approx. 12 weeks. Especially while primal. However, you may have to be incredibly strictly primal (like under 20g of carbs per day), and probably make sure the calories you ingest are the proper kind (don't ask me, others probably know better than I.)
However, what I have heard to be true is that losing more than 3lbs a week can shock your body into poor health. I don't know what the statistics of this observation are, so I can't advise you as to your chances of this happening. I also don't know exactly what kinds of poor health consequences can happen. Everyone's bodies are different and react differently, you'll have to judge for yourself.
What I ultimately recommend would be: do more strength training, and either extend your timeline by another three months or half your goal weight loss for the three months.