Combine sliced strawberries, sweetener, and vanilla extract in a bowl; allow to macerate at room temperature for 60 minutes.
Transfer the strawberry mixture to a blender. Add sour cream, lemon juice, and salt. Pulse until the mixture is mostly smooth but retains small fruit fragments.
In a large mixing bowl, whisk the heavy whipping cream and vodka (if using) into the strawberry puree until fully incorporated.
Cover the bowl and refrigerate the mixture for at least 2 hours until thoroughly chilled.
Pour the chilled base into an ice cream maker and churn according to the manufacturer's instructions, typically 20 to 25 minutes.
Transfer the churned ice cream into a freezer-safe container and smooth the surface.
Freeze for a minimum of 4 hours to reach a firm, scoopable consistency before serving.