Line an 8x8 inch baking dish with parchment paper or grease it lightly.
In a medium saucepan, combine granulated sugar, butter, and heavy cream over medium heat. Stir until the mixture is melted and well combined.
Bring the mixture to a gentle boil, stirring constantly. Allow it to boil for 5 minutes without stirring.
Remove the saucepan from heat and carefully add the lemon zest, lemon juice, vanilla extract, and salt. Stir until well combined.
Gradually add the powdered sugar to the mixture, stirring until smooth and creamy.
Pour the lemon fudge mixture into the prepared baking dish and spread it evenly.
Let it cool at room temperature for about 10 minutes, then transfer it to the refrigerator to set for at least 1 hour.
Once set, cut the fudge into squares or bars and serve.