Combine the milk, sugar, and lemon zest in a saucepan. Bring the mixture just to a simmer over medium heat. Remove from the heat.
Cover the saucepan and allow the mixture to sit for 30 minutes. Pour the mixture through a strainer into a large measuring cup.
In a bowl, whisk together the egg yolks and heavy cream. Slowly whisk the warm milk into the egg and cream mixture. Return the mixture to the saucepan.
Cook the mixture over medium-low heat, stirring constantly, until the mixture thickens. Stir in the vanilla extract. Pour the mixture into a bowl, cover and refrigerate until cold, 4-5 hours. Stir the lemon juice and a few drops of food coloring into the ice cream mixture.
Pour the mixture into an ice cream maker and churn until frozen (according to the manufacturer's instructions). Transfer to plastic container and place in the freezer for a few hours before serving.