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. Let stand until apricots are softened, about 1 hour.
While dried apricots are standing, roast whole plumcots 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 (including any liquid), plumcots, lemon juice, and almond extract in a blender until very smooth, 1 1/2-2 minutes.
Force puree through a fine sieve into a bowl, pressing hard on solids and discarding them.
Chill puree, covered, until cold, at least 2 hours.
Prepare ice cream according to manufacturer’s instructions.