Make the strawberry sauce first so that it can cool while the rest of the ice cream is being made. Put the strawberries and lemon juice in a small sauce pan and bring the heat to medium. Use a potato masher to squish the strawberries into a sauce as it cooks. Let the sauce simmer for 10 minutes to reduce down. Set the sauce aside to cool for later.
Put the rest of the ingredients into a high speed blender and puree until smooth.
Pour the ice cream mixture into your ice cream maker, and churn according to the manufacturer's instructions, until the ice cream is thick, and the consistency of soft serve ice cream. My ice cream maker takes about 30 minutes to do this.
When the ice cream is done churning, pour half of the ice cream mixture into your freezer container (see Notes for container suggestions). Spoon half of the strawberry sauce over the ice cream, and lightly swirl it so that it is distributed evenly. Then, pour the rest of the ice cream mixture into the container, and swirl the other half of the strawberry sauce into the ice cream
Freeze the ice cream at least 3 hours before serving. Let the ice cream container sit at room temp for at least 15 minutes to make scooping easier.