Empty the ice cream into a large mixing bowl and let it soften at room temperature. Place the container that you want to store your ice cream in into the freezer.
Make the jam: Bring the strawberries, sugar and lemon juice to a boil in a small saucepan until the sugar dissolves. Lower the heat to medium-low and allow to cook down, smashing the strawberries with a wooden spoon. It will thicken in about 15-20 minutes. Remove from heat. It will continue to thicken off heat.
Give the chocolate chunks a rough chop and add them to the mixing bowl of ice cream. Stir in the strawberry pieces. Remove the storage container from the freezer and pour the ice cream into the container.
Dot spoonfuls of jam onto the surface of the ice cream. Using a knife, swirl the jam through the ice cream. Cover and freeze until firm.