In a medium-sized saucepan, bring milk, lemon juice, and champagne to a simmer. Add in sugar. Separately, whisk cornstarch in 1-2 tablespoons of water, dissolving any clumps, then add to milk mixture. Cook for 3-4 minutes on medium to medium-low heat. Once the mixture starts to thicken, add in butter, vanilla, and lemon zest. Cook for 1 more minute and remove from heat.