In a medium saucepan over medium high heat, combine lemon juice and sugar. Cook undisturbed until most of the sugar is melted, about 10 minutes. Gently stir, until sugar is completely melted. Using a moistened pastry brush, wash down any sugar crystals from the side of the pan.
Add strawberries and raise heat to high and gently boil (and gently mash the strawberries) until the mixture reaches 220°-- continue to boil until thickened, about 5 minutes. Let cool about 5 minutes, then spoon the preserves into 6 very clean, 8-ounce canning jars, leaving a 1/4 inch of space at the top, and close with the lids and rings. Let cool and refrigerate or process.
To process, boil the sealed jars for 15 minutes. Let cool to room temperature and serve after 2 days or store the preserves in a cool, dark place for up to 1 year. Refrigerate after opening.