Combine figs and 3 cups sugar in a small Dutch oven, stirring mixture well. Cover and let mixture stand overnight at room temperature.
Cook fig-sugar mixture over medium heat until sugar dissolves, stirring constantly. Bring to a boil, and cook 10 minutes, stirring occasionally. Add lemon slices; cook an additional 10 minutes or until figs are tender and clear.
Carefully remove figs from syrup with a slotted spoon, and set aside; boil syrup an additional 10 minutes or until desired thickness. Return figs to syrup; skim off foam with a metal spoon.
Quickly ladle preserves into hot sterilized jars, leaving 1/4- inch head space; cover at once with metal lids, and screw bands tight.