Preheat oven to 350 degrees F. Wrap a springform pan with a few layers of aluminum foil. Bring a tea kettle of water to boil for the waterbath.
Place ladyfinger cookies in a food processor and process until fine crumbs.
Combine crumbs, butter and kahlúa together in a bowl until crumbs are moist. Press into the bottom of a 9" springform pan. Bake for 10 minutes. Remove from heat and let cool.
Meanwhile, combine cream cheese, mascarpone and sugar in the bowl of a stand-mixer (or in a large bowl if using a hand-mixer) and cream together until smooth. Add eggs, one at a time, fully incorporating each before adding the next. Make sure to scrape down the bowl in between each egg. Add heavy cream, vanilla, lemon juice, and kahlúa and blend until smooth and creamy.
Pour batter into prepared crust and tap the pan on the counter a few times to bring all air bubbles to the surface. Place pan into a larger pan and pour boiling water into the larger pan until halfway up the side of the cheesecake pan. If cheesecake pan is not airtight, cover bottom securely with foil before adding water.
Bake 45 to 55 minutes, until it is almost done - this can be hard to judge, but you're looking for the cake to hold together, but still have a lot of jiggle to it in the center. Let cool in the oven for 1 hour. After one hour, remove cheesecake from oven and lift carefully out of water bath. Let it finish cooling on the counter, and then cover and put in the fridge to chill 8 hours or overnight.
Gently loosen the edges of the springform pan and remove. Use a sifter to sift cocoa powder over the top of the cheesecake. Slice and serve.