Place ingredients in blender. Combine the 2 eggs, can of coconut milk, 1 cup flour, 2 tablespoons sugar, and 1/4 teaspoon salt in a blender.
Blend. Cover and blend on high until smooth. Let rest at least 30 minutes at room temperature.
Prep strawberries. Slice the quart of strawberries and combine with remaining 2 tablespoons sugar, 1/2 teaspoon lemon zest, and 2 teaspoons lemon juice in a medium bowl. Stir until strawberries are coated in sugar, set aside.
Cook crepes. Heat 1/2 teaspoon of the oil in a medium nonstick frying pan over medium heat. Once oil is shimmering, whisk batter one more time, then pour in 1/4-1/3 cup of the batter, swirling so the batter covers the entire surface in a thin layer. Add the larger amount if you pan is bigger.
Flip and repeat. Cook the crepe undisturbed for 2 minutes or until the bottom is lightly browned and crisp and the top seams almost dry with a few wet spots. Flip or turn the crepe and cook about 1 minute more or until toasted on the other side. Repeat with the remaining batter, stacking the crepes with parchment paper in between to prevent them from sticking together; you should have 8-10 crepes.
Fill and enjoy! Give the strawberries a stir and taste, adding more lemon juice or sugar as needed. Lay one crepe on a plate and put a spoonful of strawberries with some of their juice and a sprinkling of toasted coconut in one corner of the crepe. Fold the crepe in half to cover the berries and spoon some more berries and coconut on top of that. Fold the crepe over one more time to enclose the filling and top the crepe with a final spoonful of berries, a sprinkling of coconut and a few lemon zest strips. Serve immediately.