Place the eggs, milk, water, melted butter, flour, and salt in the pitcher of a blender; blend until smooth.
Blend the cream cheese, confectioners' sugar, lemon juice, lemon zest, and vanilla with an electric mixer until smooth. Gently fold in the whipped cream.
Heat a lightly oiled griddle or non-stick skillet over medium heat. Pour or scoop the batter onto the griddle, using approximately 2 tablespoons for each crepe. Tip and rotate pan to spread batter as thinly as possible. Flip over when the batter is set and the edges are beginning to brown. Cook until the other side begins to brown. Stack finished crepes on a plate, cover with a damp towel and set aside.
To serve, fill each crepe with 1/4 cup sliced strawberries and 1/3 cup of the cream cheese filling, roll up and top with a small dollop of the cream cheese filling and more sliced strawberries.