Heat oven to 325 degree F. Place cookie crumbs in a bowl. Melt butter and stir into crumbs. Press mixture into bottom of an 8-inch springform pan. Bake at 325 degrees F for 10 minutes. Remove to a wire rack to cool.
In a large bowl, beat together cream cheese and sugar until smooth. Beat in eggs, one at a time, until blended, then beat in flour. Stir in lemon zest and juice. Pour into pan, spreading level.
Return to oven and bake at 325 degrees F for 40 to 45 minutes, until lightly golden around edges. Remove to rack to cool.
In a small saucepan, combine sugar, rhubarb and 1/4 cup of the strawberries. Bring to a low boil over medium-high heat. Continue to cook, stirring, an additional 6 to 7 minutes. One minute before finished, add remaining 1/2 cup berries. Remove from heat.
As soon as cheesecake is baked, spread with warm topping, leaving a border around edge. Run a thin knife between pan and cake; cool to room temperature. Chill at least 2 hours, or until serving.