Preheat oven to 350 degrees. Spray a 9 X 13 inch baking dish with nonstick cooking spray.
Using a stand mixer (if you have one), beat butter until creamy. Slowly add sugar then continue to beat until it's fluffy. Add eggs one at a time, and beat after each until incorporated. Add lemon juice and vanilla and mix in.
In another bowl combine flour, strawberry jello, baking soda and salt. Add the flour mixture to butter mixture alternating with the buttermilk (a little at a time of each) until mixed well. Gently stir in strawberries.
Pour batter into prepared baking pan and bake in preheated oven for 35-40 minutes or until a toothpick inserted in the center of the cake comes out clean. Cool cake completely.
For the frosting:
In a large bowl, beat the cream cheese with 1/3 cup of sugar until mixture is smooth. Fold in strawberries.
In another bowl, beat the whipping cream and lemon juice until mixture is frothy. Continue beating on medium-high speed and gradually add the remaining 1/3 cup sugar. Beat until mixture forms stiff peaks. Fold half of whipped cream mixture into the cream cheese mixture until just incorporated. Fold in the rest of the whipped cream mixture.
Spread on top of the cake and serve immediately. Refrigerate any leftovers.