Whisk together lemon juice, sugar, salt, cumin, and cayenne in a large bowl until sugar and salt are dissolved. Add carrots and figs and toss well. Let stand, uncovered, at room temperature, tossing occasionally, until carrots are wilted, about 30 minutes.
Makes about 3 cups.
Gourmet
Active time: 20 min.
Start to finish: 50 min.