Line a colander or mesh sieve with a coffee filter, or cheesecloth, and place in a bowl. Add the yogurt to the colander/sieve and allow to drain for at least 4 hours, or ideally, overnight. Discard the drained liquid.
In a small saucepan, add milk, and sprinkle with gelatin. Allow to sit and soften for 5 minutes.
Add the strip of lemon rind, sugar and vanilla to the saucepan with the milk and gelatin. Heat over medium-low, and cook just until the sugar and gelatine have dissolved. Set aside to cool to room temperature. Remove the lemon rind.
Once cooled, add the strained yogurt, and stir to combine. Press the mixture through a mesh sieve. This will catch any lumps of gelatin, and create a smooth mousse.
In a separate bowl, whip the cream to stiff peaks. Then, gently fold it into the yogurt mixture.
Spoon into parfait cups and chill for at least 4 hours.