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Venison is very lean, and any fat it does have, you do not want to eat as that stuff is just plain nasty and needs to be trimmed off'! That being said, you would likely want to add some fatty pork to the meat when you grind it up. I suspect the burger would be a bit chewey as well. Venison does best not cooked beyond Med rare. I never any grind it for anything except for summer sausage. YMMV
I would try chorizo with the verison. I make a meat loaf with turkey breast which is very lean 99% and add chorizo to it and they come out great. The turkey to chorizo ratio is about 2 to 1, 2 being the turkey.