Bring sugar, water, and dried apricots to a boil in a 3-quart heavy saucepan over moderate heat, stirring, until sugar is dissolved.
Remove from heat and let stand until apricots are softened, about 1 hour.
While dried apricots are standing, roast whole fresh apricots in a small roasting pan in middle of oven until soft, about 1 hour. Cool in pan, and pit when cool enough to handle.
Puree dried apricot mixture, roasted apricots, lemon juice, and almond extract in a blender until very smooth, 1 1/2 to 2 minutes. Force puree through a fine sieve into a bowl, pressing hard on solids and then discarding them. Chill puree, covered, until cold, at least 2 hours.
Freeze in ice cream maker, then transfer to an airtight container, and put in freezer to harden.
Cook's note: Puree can be chilled up to 8 hours. Sorbet keeps 1 week.
