Whisk the Greek yogurt, sweetener, vanilla extract, lemon juice, and salt in a large mixing bowl until the sweetener is completely dissolved and the mixture is smooth.
Cover and refrigerate the yogurt mixture for at least 1 hour to ensure it is thoroughly chilled.
Turn on an ice cream maker and pour the chilled mixture into the frozen canister.
Churn the mixture according to the manufacturer's instructions, typically 20 to 25 minutes, until it reaches a soft-serve consistency.
Transfer the frozen yogurt to an airtight container and freeze for an additional 2 hours for a firmer, scoopable texture.