Place apples and juice in heavy saucepan. Cover and cook over moderate heat until very tender – about 15 minutes.
Process apple mixture in food processor until very smooth. (I skipped this step and went right to to the sieve). Strain through a fine strainer pushing down on solids to extract as much puree as possible.
Stir in lemon juice and Calvados (if using).
Cool. Freeze in ice cream maker according to manufacturers instructions.