In a large bowl, use an electric hand mixer or a stand mixer to beat together the cream cheese and sugar until smooth and creamy. Use a spatula to scrape down the sides of the bowl, as necessary.
Mix in the Greek yogurt, vanilla extract, lemon zest, and lemon juice just until combined. Gradually add the heavy cream (about ¼ cup at a time), whipping it into the cream cheese mixture after each addition.
Pour the batter over the graham cracker crust. Spread into an even layer (an offset spatula makes this task easy!). Cover and chill in the refrigerator for at least 8 hours or overnight, until fully set.
Carefully lift the bars out of the pan by holding onto the edges of the parchment paper. Slice the bars into squares, wiping the knife clean after each slice. Top with whipped cream, Cool Whip, lemon slices, or fresh berries if desired.