Chop and mash 1 pint (2 cups) strawberries in a large bowl. Stir in 1/4 cup sugar, 1 teaspoon vanilla, and lemon juice. Halve remaining 2 pints (4 cups) strawberries; add to mashed strawberries. Set aside.
Heat milk in a medium saucepan over medium heat until hot (do not boil). Combine eggs and 1/3 cup sugar in a medium saucepan; stir well with a whisk. Gradually add hot milk, stirring well. Cook, stirring constantly, over medium heat 6 minutes or until mixture coats back of a spoon (do not boil). Remove from heat, and let cool.
Stir in 2 teaspoons vanilla extract. Cover and chill thoroughly. Spoon crème anglaise over berries to serve.