Preheat your oven to 325°F (163°C). Line the muffin tin with cupcake liners if desired.
In a mixing bowl, combine the graham cracker crumbs, melted butter, and sugar, mixing until well combined.
Press the crumb mixture into the bottom of each muffin cup to form a crust layer. Bake in the preheated oven for 10 minutes. Remove and set aside to cool.
In a separate bowl, beat the softened cream cheese and sugar with an electric mixer until smooth.
Mix in the vanilla extract and lavender buds, then add the eggs one at a time, beating well after each addition.
Stir in the sour cream until incorporated.
Pour the cheesecake filling over the cooled crusts in the muffin tin, filling each cup about ¾ full.
Bake for an additional 15-20 minutes, or until the centers are set but still slightly jiggly. Remove from the oven and let them cool for a few minutes.
Refrigerate the cheesecakes for at least 2 hours to set properly.
Meanwhile, prepare the blackberry sauce. In a saucepan over medium heat, combine blackberries, sugar, and lemon juice. Cook until the blackberries break down and thicken, about 5-7 minutes. Strain the sauce through a fine-mesh sieve if desired to remove seeds.
Once the cheesecakes are fully chilled, top with the blackberry sauce before serving.