Put the strawberries and bananas on a baking sheet in the freezer for an hour. To save this step, you can make up pre-portioned out bags ahead of time so you can just pull out a bag when you want to make your sorbet!
Once the fruit has been in the freezer for at least an hour, put it in your food processor or blender along with the lemon juice from one lemon and process until smooth – scrape down the sides when you need. The sorbet will be soft serve style texture right out of the blender, or you can put it in the freezer to firm up for a bit if you want.