Tie ginger and cinnamon stick in a cheesecloth bag. Set aside.
Place sugar and lemon juice in a large non-reactive stockpot. Heat, adding just enough water to dissolve the sugar. Add spice bag, figs, and lemon slices. Bring to a boil, reduce heat, and simmer at a low boil about 45 minutes, stirring often to prevent sticking.
Remove and discard spice bag. Spoon hot fig preserves into hot, sterilized canning jars. Wipe rims clean and seal immediately with hot, sterilized lids. Process in boiling water bath for 5 minutes for half-pints or 10 minutes for pints.