In a mixing bowl, combine the eggs, milk, water, and melted butter, whisking until well incorporated. In a separate bowl, combine the flour and salt, then gradually add the dry ingredients to the wet mixture, stirring until smooth. Cover and refrigerate for at least one hour to allow the batter to rest.

Heat a lightly greased nonstick skillet (8-inch in diameter) over medium heat. Stir the batter before using. Using a 1/4-cup measuring cup, pour the batter into the center of the pan. Quickly tilt and swirl the pan to spread the batter evenly. Cook until the surface appears dry, then flip the crepe and cook for an additional 15-20 seconds. Remove the crepe to a wire rack and continue with the remaining batter, greasing the pan as necessary. Allow the crepes to cool, stacking them between wax paper or paper towels.

For the filling, combine the softened cream cheese, powdered sugar, lemon juice, lemon zest, and vanilla extract in a small bowl, beating until smooth and well combined. Gently fold in 2 cups of the sliced strawberries and the whipped cream. Spoon approximately 1/3 cup of the filling onto the center of each crepe, then roll it up. Garnish with the remaining strawberries and, if desired, dust with additional powdered sugar. Cover and refrigerate or freeze any leftover unfilled crepes in an airtight container for later use.