1. Cut the lemons in half and ream juice from them. Pour the juice through a fine-mesh strainer into a measuring cup and discard the seeds and pulp. You should have 1/2 cup. Cover and refrigerate.
2. Place 4 cups water, 3/4 cup sugar, salt, and strawberries in a pan and bring to a boil over medium-high heat. Stir often with a spoon and, using the back of it, crush the berries. Continue to boil, stirring often, until the sugar has dissolved, about 2 minutes. Let cool, cover, and refrigerate until well chilled.
3. Pour the chilled syrup through a fine-mesh strainer into a pitcher; discard the pulp. Add the lemon juice to syrup and stir well. Taste, and adjust to desired sweetness.
4. Pour lemonade into glasses. Serve with ice cubes and garnish with thin lemon slices.