Add the cream cheese, sugar, coconut oil, lemon juice/zest and vanilla extract to a food processor or blender. Blend until smooth.
Add the strawberries and a dash of water to a medium-size saucepan over high heat. Simmer and mash with a fork or stick blender to help the strawberries break down. Cook for 10-15 minutes or until the mixture has reduced to around ½ cup, heaped (~180g). It should be the texture of tomato pasta sauce.
Add the coconut cream and corn starch/flour to the saucepan and whisk thoroughly. Bring it to a gentle boil for 5 minutes or until the mixture thickens up. The mixture may seperate which is normal!
Add the strawberry mixture to your food processor/blender and blend until as smooth as possible. If desired, add beetroot powder to colour. Pour the cheesecake filling into your cake tin and smooth the top. Chill the cheesecake the fridge for 4 hours or until set.