Using vegetable peeler, remove peel from lemons (yellow part only) in long strips. Cut peel into matchstick-size strips (about 3 tablespoons).

Combine lemon peel, figs, sugar, brandy, and 1/2 teaspoon coarse salt in heavy large deep saucepan; let stand at room temperature 1 hour, stirring occasionally.

Bring fig mixture to boil over medium-high heat, stirring until sugar dissolves. Reduce heat to medium; continue to boil until jam thickens and is reduced to 6 cups, stirring frequently and occasionally mashing mixture with potato masher to crush large fig pieces, 30 to 35 minutes. Remove from heat.

Ladle mixture into 6 hot clean 1/2-pint glass canning jars, leaving 1/4-inch space at top of jars. Remove any air bubbles. Wipe jar threads and rims with clean damp cloth. Cover with hot lids; apply screw bands. Process jars in pot of boiling water 10 minutes. Cool jars completely. Store in cool dark place up to 1 year.