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.