Combine two-thirds of the strawberries and half the sugar in a blender and puree until smooth. Add more sugar to taste. Press the pureed strawberries through a fine sieve to remove the seeds.
Just before serving, whip the cream in a large bowl until stiff. Coarsely chop the remaining strawberries. Dust the chopped berries with a little sugar and sprinkle with the lemon juice. Gently fold the pureed and chopped strawberries into the cream and serve.