Line a small sheet pan with parchment paper and place it in the freezer. Beat cream cheese, powdered sugar, and lemon juice until smooth. Scoop 2-teaspoon dollops onto the pan and freeze for 60 minutes.
After 30 minutes, line a cookie sheet with parchment paper. Do not preheat the oven yet.
Whisk flour, baking soda, and salt together in a bowl. Set aside.
In another bowl, beat butter and granulated sugar until smooth. Add brown sugar and beat until creamy.
Mix in egg and vanilla extract until combined.
Add dry ingredients and mix on low speed until just combined.
Reserve 12 freeze-dried strawberry slices, then gently mix the rest into the dough.
Scoop 1 tablespoon of dough, place a frozen cheesecake dollop on top, and add one reserved strawberry slice.
Cover with another tablespoon of dough, seal edges, and roll into a smooth ball. Repeat to make 12 cookies.
Chill the cookie dough balls for 30 minutes.
Preheat oven to 350°F. Place 6 cookies per baking sheet, top with graham cracker pieces, and bake for 11–13 minutes.
Cool completely on the baking sheet before serving.