Combine sugar and water in a heavy saucepan; cook over medium heat, stirring constantly, until sugar dissolves.

Remove sugar syrup from heat; cool.

Place thawed strawberries in container of an electric blender or food processor; process until smooth.

Pour through a wire mesh strainer into a 8-inch square pan, pressing with back of spoon against the sides of the strainer to squeeze out juice.

Discard pulp and seeds.

Stir lemon juice, sugar syrup, and champagne into strawberry puree.

Cover and freeze at least 4 hours.

Position knife blade in food processor bowl; add frozen mixture, and process until smooth.

Return to pan and freeze until firm.

Repeat processing procedure, and return mixture to pan; freeze until firm.

Spoon into glasses, and serve with fresh strawberries.