Put oven rack in middle position and preheat oven to 350°F. 3Boil water and 1/2 cup sugar in a small saucepan, stirring, until sugar is dissolved.
Remove syrup from heat. Squeeze enough juice from 2 lemons to measure 1/3 cup and stir into syrup, then discard lemon halves.
Remove zest from remaining lemon in long strips with a vegetable peeler and, if necessary, trim any white pith from zest with a sharp paring knife.
Cut zest lengthwise into thin julienne strips. Reserve lemon.
Blanch zest in a 1- to 1 1/2-quart saucepan of boiling water 1 second, then drain in a sieve and add to syrup. 3
Cut away any remaining pith from lemon. Working over a bowl, cut segments free from membranes.
Spread butter in a 1 1/2-quart flameproof gratin dish or 10-inch heavy ovenproof skillet. Arrange figs, cut sides up, slightly overlapping in 1 layer.
Sprinkle with remaining 2 teaspoons sugar and bake until figs are softened and begin to exude juice but still hold their shape, 25 to 30 minutes.
Transfer figs with a slotted spoon to a shallow serving bowl and put gratin dish or skillet over a burner at moderately high heat.
Add syrup and deglaze gratin dish or skillet by boiling until syrup is reduced to about 3/4 cup, 6 to 8 minutes.
Add lemon segments along with any juices in bowl and pour syrup (with lemon segments) over figs. Cool to warm or room temperature before serving.
Syrup can be made, without deglazing and adding lemon segments, 1 day ahead and cooled completely, uncovered, then chilled, covered. Bring to room temperature before deglazing gratin dish and adding lemon segments.
