A full 24 hours before you make your frozen yogurt, place your ice cream maker insert into the freezer.
Add strawberries, sugar, lemon zest, lemon juice, and rum to a bowl and toss. Cover with plastic wrap and let the strawberries macerate at room temperature for 1 hour.
Add the strawberries with their juices to a food processor. Pulse the berries, and then add the vanilla beans seeds and yogurt. Continue to blend until smooth.
Place in the refrigerator to chill for 1 hour.
Turn your ice cream machine on and pour in the chilled yogurt mixture. Churn until the mixture looks slushy like soft serve, about 12 to 15 minutes.
Place in the freezer for several hours until hard enough to scoop.