Whisk together powdered sugar, lemon juice, and vanilla. Drizzle over cooled cake and let glaze harden for at least 10 minutes.
Transfer to a serving platter and serve with fresh strawberries if desired.
Instant lemon pudding: Can't find lemon pudding? Vanilla tastes great too! Most of the lemon flavor comes from the cake mix, so you don't lose too much flavor with vanilla pudding. I tested this to make sure.
Vegetable oil: Readers have reported that substituting 1/2 cup applesauce for the 1/2 cup oil works perfectly. To quote Karen from the comments, "[I] saved over 800 calories per whole cake without any noticeable difference in taste or texture."
Lemon zest: Zest the lemons before you cut them in half for juice. To zest a lemon, hold a grater in one hand and the lemon in the other over a cutting board or clean work surface. Going in one direction, push the lemon away from you across the rough side of the grater, removing the colorful part of the fruit, exposing the pith. Gently rotate the lemon as you go.
Yield: This recipe makes 12 slices (or fewer bigger slices, depending on how you cut them).
Storage: Store leftovers covered at room temperature for 3 to 4 days.