For the batter: In a bowl, whisk together the eggs, milk, flour and sugar until smooth and let stand 20 minutes.
For the compote: Peel the apples, remove the seeds and cut into chunks. In a saucepan, bring the apple juice, cinnamon, sugar and lemon zest and juice to a boil, let it boil a little, then add the apple pieces and simmer until the apples are falling apart, about 10 minutes. Remove the cinnamon stick and set aside.
Heat some butter in a skillet and working in batches, drop about 1/8 of the batter into the skillet, swirl the pan until coated and cook the crepes until golden brown on each side. Repeat with more butter and the remaining batter.
Fill the crepes with the lukewarm compote, roll them up and serve arranged on plates.