Combine the cookie crumbs, sugar, and melted butter until thoroughly combined. Press into the bottom and partially up the sides of a 9-inch springform pan. Place the pan on a rimmed baking sheet to catch any potential spills or leaks.

Bake 15 minutes. Set aside to cool.

Using an electric mixer on medium speed, beat the cream cheese, sugar, and cornstarch until thoroughly combined and smooth. Add the eggs, one at a time, mixing well after each addition. Mix in the sour cream, pineapple juice, and vanilla extract.

Pour into the pan, and smooth the top.

Bake 15 minutes.

Remove the cheesecake from the oven, and run a thin knife around the edges. Return it to the oven, turn off the oven, and leave for 2 hours.

Refrigerate overnight.

In a small bowl, mix the cornstarch and water until smooth. 

In a small saucepan, combine the drained crushed pineapple and sugar over medium heat. Stir occasionally until the sugar has dissolved.

Add the cornstarch mixture to the saucepan with the pineapple mixture, stirring constantly.

Bring the mixture to a boil, then reduce the heat to low. Simmer for about 2-3 minutes, or until the mixture has thickened.

Remove the saucepan from the heat and stir in the lemon juice.

Allow the pineapple topping to cool completely before spreading it over your cheesecake.