Combine sliced strawberries and sugar, mixing well, set aside for 5 minutes.
Combine lemonade concentrate and sliced strawberries, stir well.
Spoon about 1 1/2 tablespoons strawberry mixture into each of six 6-ounce parfaits, top with 1/2 cup ice cream.
Top with remaining strawberry mixture.
Freeze until firm.
Before serving, top each parfait with whipped cream and a whole strawberry, if desired.