Slice the strawberries and toss them with the sugar, if you are using sugar. Let it sit at room temperature until the sugar has dissolved into the strawberry juices, about an hour.
Pulse the strawberries in their juices with the sour cream, fresh cream, and lemon juice in a blender until they are smooth, with little chunks of strawberry.
Refrigerate mixture for at least one hour, covered.
Pour the mixture into your crank freezer or electric ice-cream maker and follow the manufacturer’s directions. If you do not have an ice cream maker, you can improvise by filling a quart-size zipper-style bag two-thirds full with the ice cream mixture and zipping it closed, then putting it into a gallon-size zipper-style bag. Hold the mouths of the bags flush while somebody else fills the gallon-sized bag with crushed ice and rock salt, in layers. Zip the gallon-sized bag closed and begin to massage and shake the bags to achieve the same effect as from a classic ice cream freezer. You may have to do a few batches this way. Keep checking the quart bag to see if your ice cream has frozen sufficiently.
Pack ice cream into a quart-size lidded container. Cover with plastic wrap, pressing it onto the surface of the ice cream. Place the ice cream into the freezer and leave until fully set, about 5 to 6 hours, or overnight.