Preheat the oven to 350 degrees F. and grease an 9x9 inch pan.
Stir the crushed graham crackers and melted butter together and press into the prepared pan. Bake for 10 minutes then remove and allow to cool.
In a pot, cook the mangos over low-medium heat until soft, about 10 minutes. Use an immersion blender or a blender to blend them until smooth. Place them back in the pot.
Stir the arrowroot and water together and pour into the pot. Allow the mangos to simmer until thickened, then remove from the heat. Allow to cool completely.
In a large bowl, beat the cream cheese until smooth. Add half of the condensed milk and beat, then add the remaining half and beat.
Add the eggs, lemon juice, and vanilla and beat until smooth.
Remove ¼ cup of the cream cheese mixture and add it to the mango puree. Stir together until smooth.
Pour the remaining cream cheese mixture over top of the crust.
Place the mango puree in a zip top bag and cut one end off. Squeeze the mango puree in a zig-zag pattern over top of the cheesecake batter. Use a toothpick and run it along the mango puree to create a swirl pattern.
Bake the cheesecake for 35-45 minutes, until the edges are set and the center is slightly jiggly. Then crack the oven door, turn the oven off, and leave it in there for 1 hour.
Afterward, remove it from the oven and let cool completely. Then cover and refrigerate until fully chilled, at least 4 hours.
Cut after it has chilled.