Heat oven to 350°F. Spray bottom and sides of a 13x9-inch baking pan with cooking spray.
In a large bowl, whisk flour, powdered sugar, baking soda and 1/4 teaspoon salt until well combined.
Cut in cold butter with a pastry blender or two knives until mixture resembles coarse crumbs.
Press mixture evenly in bottom of prepared baking pan (the mixture will seem loose, but it hardens as it bakes and cools). Bake for 15-20 minutes until the crust is a light golden brown. Transfer to a cooling rack while you prepare the filling.
Slice both rhubarb and strawberries into ¼ inch pieces. If the rhubarb is still green, peel with a vegetable peeler.
In a medium saucepan, stir together 3/4 cup granulated sugar, cornstarch and 1/4 teaspoon salt. Stir in rhubarb and 6 ounces strawberries. Let stand for 15 minutes, stirring occasionally.
Bring mixture to a boil over medium heat, stirring constantly. Reduce heat to low; simmer 3-5 minutes, stirring constantly, until thickened. Remove from heat; stir in vanilla and remaining 6 ounces strawberries.
In a medium bowl using an electric hand mixer, beat cream cheese and 3/4 cup granulated sugar on medium speed until smooth. Scrape down the sides of the bowl with a silicone spatula.
Beat in eggs one at a time, then beat in lemon zest and juice.
Spread strawberry-rhubarb filling over crust in baking pan. Carefully spread cheesecake topping over strawberry-rhubarb filling to edges of pan. Bake at 350 degrees F 25-30 minutes until cheesecake topping is just set. The center will have a slight jiggle, like jell-o.
Cool on cooling rack 1 hour; cover and chill 4-8 hours.