Step 1Bring a small saucepan of water to a boil. Meanwhile, remove any seeds from the lemon slices. Add the slices to the boiling water, stir for 10 seconds, then use a spider or slotted spoon to remove the slices and transfer to a bowl. Discard the water and refill the pan with fresh water. Repeat this blanching process two more times, making sure to start with fresh water each time (this removes most of the bitterness from the lemon pith).
Step 2Pour 2 cups fresh water into the pan, then stir in the sugar. Bring to a boil over high heat, stirring to dissolve the sugar. Reduce the heat to medium-low, add the lemon slices and cook, maintaining a steady, gentle simmer and stirring occasionally, until the slices are tender and fully translucent but not falling apart, about 30 minutes.
Step 3Remove the pan from the heat and let the slices cool completely in the syrup. Use a fork to transfer the slices to a plate and discard the syrup or save for another use.
Step 1Pour 2 teaspoons cold water into a small bowl. Sprinkle the gelatin over the top, then stir to ensure the gelatin is evenly moistened; let stand while you make the curd, at least 5 minutes.
Step 2In a medium bowl, whisk the sugar and eggs vigorously until smooth and lightened in color, about 1 minute, then whisk in the lemon juice. Fill a saucepan with 1 inch of water and bring to a boil over high heat. Reduce the heat to medium, place the bowl over the pan (make sure the bottom does not touch the water) and cook, whisking steadily, until the curd thickens to the consistency of mayonnaise, 3 to 4 minutes (an instant-read thermometer inserted in the curd, but not touching the bowl, should read 170 degrees).
Step 3Remove the bowl from the pan, add the gelatin and stir until dissolved. Continue stirring the curd until cooled to 130 degrees, 2 to 3 minutes. Add one piece of butter and whisk until it fully melts into the curd; repeat with the remaining butter, making sure each piece melts fully before adding the next. Place a sheet of plastic wrap directly on the surface of the curd, then refrigerate it until thickened and set, at least 8 hours or overnight.