I understand you want to determine LD50 of SM testing on mice (or other animal). In fact, no need to do it. Usually, this parameter is needed to test for any substance or compound isolated from mushroom but not with whole. Shitake (lentinus edodes) is edible foodstuff like rice, corn. When you feed the mice, the animal will be suffered other stronger stress and to be sicked and died by feed full but not from toxins.
Side effects of shiitake mushrooms are very rare. We followed health impairments of mushrooms by cases of German poisons centres as well as from reports of German physicians. We never saw and we never heard of lethal posionings with shiitake mushrooms in humans in Germany.