Throw the apples, apple juice and lemon juice into a pan and bring it to the boil over medium-high heat. Lower the heat and simmer until the apples are soft, about 15 minutes. Stir through the sugar and mix until melted. Add the cinnamon and stir through.
Puree the mixture in a food processor, blender or food mill. If not using right away, leave to cool and then refrigerate.
When blending hot liquid, first let it cool for five minutes or so, then transfer it to a blender, filling only halfway. Put the lid on, leaving one corner open. Cover the lid with a kitchen towel to catch splatters, and pulse until smooth.