For topping: Rinse and dry orange. With a sharp knife, slice into thin rounds (between 1/8 and 1/16 in. thick; see Notes), discarding ends and seeds. In a deep 10-in. frying pan or pot over medium-high heat, stir sugar, 3/4 cup water, and lemon juice until sugar is dissolved. Add orange slices and bring to a simmer. Cover and simmer 5 minutes. Uncover and simmer gently, keeping slices in a single layer and turning occasionally, until they're slightly candied and translucent and liquid has the consistency of a thin syrup, about 20 minutes (there should be about 1/2 cup liquid in pan; if less, add enough hot water to make that amount and shake pan to mix water into syrup). Let cool in pan. Cover and chill at least 15 minutes and up to 2 days.
For cheesecake: Preheat oven to 300°. Pour graham cracker crumbs into a 9-in. cheesecake pan with removable rim; add butter and mix. Press mixture evenly over bottom and 1/2 in. up sides of pan.
In a large bowl, with a mixer on medium speed, beat cream cheese and sugar until smooth. Add eggs 1 at a time, beating after each addition. Beat in flour, sour cream, and liqueur just until incorporated. Pour into crust-lined pan.
Bake until center barely jiggles when cake is gently shaken, 60 to 70 minutes. Run a thin-bladed knife between cake and pan rim. Cool completely at room temperature, then cover and chill until cold, at least 3 hours or up to 2 days.
Remove pan rim. If any moisture collects on top of cake, gently blot dry. Gently lift candied orange slices from syrup, reserving syrup, and blot dry with a paper towel. Arrange slices, slightly overlapping, over top of cheesecake.
Measure orange juice. Bring reserved syrup to a boil over high heat. Stir occasionally until syrup is deep golden brown, 1 to 3 minutes. Remove from heat and carefully stir in orange juice (mixture will bubble up). Let cool to room temperature and generously brush over orange slices (you may have extra syrup).
Serve cheesecake, or cover and refrigerate up to 2 days. Use a serrated knife to cut cake, wiping blade clean after each slice.
Note: Nutritional analysis is per slice.