Prepare the strawberries: Combine 4 cups strawberries and the granulated sugar in a large saucepan over medium heat. Cook until bubbling, then increase the heat to medium high and cook, stirring occasionally, until the berries are soft and the liquid is thick enough to coat the back of a spoon, about 15 minutes. Remove from the heat and stir in the remaining 2 cups strawberries and the lemon juice. Let cool, then transfer to a bowl, cover and refrigerate at least 1 hour or overnight.
Meanwhile, make the crumble: Preheat the oven to 350 degrees F. Generously butter a 9-inch-round cake pan. Combine 3 cups pretzels, the melted butter, egg white, granulated sugar, flour and 1/4 teaspoon salt in a food processor; pulse until a wet dough forms. Press the dough evenly into the prepared pan. Break the remaining 1/2 cup pretzels into pieces and press into the dough. Bake until golden, 25 to 30 minutes. Transfer to a rack and let cool completely in the pan, then break into bite-size pieces.
Make the cream: Just before serving, beat the cream cheese, confectioners' sugar and vanilla in a large bowl with a mixer on medium-high speed until smooth, about 2 minutes. Beat the heavy cream in another bowl with a mixer on medium-high speed until soft peaks form, about 3 minutes. Gently fold half of the whipped cream into the cream cheese mixture, then fold in the rest.
Layer the cream, crumble and strawberry mixtures in individual glasses or bowls. Cover and chill, at least 1 hour and up to 6 hours.