In a saucepan, combine the strawberries, lemon juice and sugar. Cook over medium heat until the strawberries begin to soften, about 10 minutes. Remove the pan from the heat. Place the strawberry mixture in a food processor and process until smooth. Remove the mixture from the food processor and strain through a fine mesh strainer. Mix in the sliced strawberries and place in the refrigerator. Refrigerate until very cold. With an electric mixer, whip the cream. In parfait glasses, layer the strawberries and whipped cream, starting and ending with the whipped cream. Place in the refrigerate and chill for 4 hours.
Remove the zest of the lemons using a vegetable peeler. Be careful not to get any of the white pith. Julienne the zest. Blanch the julienned zest in boiling water for 5 minutes to remove any bitterness. In a small saucepan, combine 1 cup of sugar and the water. Bring to a boil. Add the blanched zest to the sugar syrup. Remove the sugar syrup from the heat and let the zest steep for 10 minutes. Remove the zest from the syrup and lay out on a rack. Sprinkle with the remaining 1/4 cup sugar.
Top the parfaits with some of the candied lemon zest.