In a small saucepan, warm blood orange juice and sugar over medium-high heat, stirring to dissolve sugar. Bring mixture to a boil and cook until reduce by 1/2. Remove from heat and let cool completely.
In a large bowl, whisk together reduced blood orange juice and Greek yogurt until smooth and fully incorporated. Add zest and liqueur, whisking to combine. Add a few drops of fresh lemon juice and a small squidge of honey, then whisk and taste. If the mixture is too tart, add a bit more honey. If the mixture is too sweet, add a bit more lemon juice.
Refrigerate mixture for at least 4 hours (preferably overnight). Freeze the yogurt base in an ice cream maker according to the manufacturer’s instructions. Finish by freezing the yogurt until hard or enjoy soft immediately.