Make the churros: In a small saucepan, combine water, butter, brown sugar and salt and bring to a simmer until butter is melted. Turn off heat and pour into a stand mixer bowl fitted with the paddle attachment. Allow to cool for 5 minutes and then add flour. Mix until combined. Add eggs and vanilla and stir. Transfer to a pastry bag with a star tip.
Preheat oven to 375 degrees, and line two baking sheets with silicone baking mats. Pipe spiral churros about 2 1/2 inches in diameter, approximately 12 round churros. Bake for 20 to 25 minutes until slightly crispy. Once slightly cooled, toss churros in cinnamon sugar and set aside.
Make the filling: In a large bowl, beat softened cream cheese with a hand mixer until light and fluffy, approximately 3 minutes. Add sweetened condensed milk, lemon and vanilla. Mix until combined. Set bowl in the freezer and allow to chill and set.
Assemble the churros: Place cheesecake filling in a piping bag, and pipe approximately 1/2 cup of filling between two churros. Dip sides of filling in graham crackers or strawberries and serve.