Cut them into large pieces and place them in a large saucepan. Add the sugar, lemon juice, honey, and lavender flowers.
Cook over low heat for 30 minutes, stirring regularly and leaving the pan uncovered.Blend the mixture and let it cool.
Add the cream and mix (or blend) until smooth.Refrigerate for 1 hour.
Pour the mixture into the bowl of your ice cream maker (which has been in the freezer overnight) and churn until the desired consistency is reached (40 minutes for me).
Transfer to a suitable container and place in the freezer for at least 1 hour.Remove from the freezer 10 minutes before serving.