Heat overn to 375 degrees. Spray 9-inch springform pan with cooking spray, or wipe evenly with butter.
In medium mixing bowl, whisk together flour, baking powder and salt.
In small bowl, combine melted butter, olive oil and lemon juice.
In bowl of stand mixer fitted with whisk attachment, combine sugar and lemon zest on low speed. Add the eggs and mix on medium-high speed until the mixture is smooth and pale yellow, about 4-5 minutes.
Add the milk and vanilla extract; mix until combined.
Reduce speed to low and add flour mixture, beating together until moistened.
Slowly add the butter and oil mixture, beating just until it is incorporated.
Pour batter into the pan and bake for 30 minutes. Check cake at 25 minutes. When done, the cake should spring back when pressed with in the center.
Prepare lemon syrup by heating 1/4 cup water, sugar, lemon juice in small pan. Heat on medium low until sugar is dissolved. Set aside, and cover to keep warm.
After cooled, remove cake from pan.
Gently drizzle and brush lemon syrup over the top and sides of *warm* cake.