Purée strawberries in a blender. Set a fine strainer over a bowl; strain strawberry purée, discarding solids. Whisk in sugar, heavy cream, and lemon juice until sugar dissolves. Pour strawberry mixture into four 3–oz. ice-pop molds.
Transfer molds to the freezer and freeze until slushy, about 1 hour. Insert a Popsicle stick into each mold and freeze until pops are solid, about 3 hours more. To release ice pops from molds, run the bottom of the molds briefly under warm water.