If using strawberries, hull and slice them before cooking. If using frozen berries, thaw them before beginning.
In a medium saucepan, combine the berries, water, 5 tbsp granulated sugar, and salt.
Place the saucepan over medium heat and bring the mixture to a bare simmer, stirring occasionally.
Continue cooking for about 1 minute, or until the sugar has dissolved and the berries are heated through.
Transfer the warm berry mixture to a blender or food processor. Puree until smooth, about 20 seconds.
Pour the puree through a fine-mesh strainer into a small bowl. Press and stir the mixture with a spoon to extract as much smooth puree as possible.
Discard the seeds and remaining pulp.
Stir the lemon juice into the strained berry puree.
Taste the coulis and add additional sugar, if desired, until the preferred sweetness is reached.
Cover the bowl with plastic wrap and refrigerate until cold, at least 1 hour.
Before serving, stir the coulis to recombine. If the sauce is too thick after chilling, stir in 1 to 2 tsp water until it reaches the desired consistency.
Serve chilled as a sauce for desserts, breakfast dishes, or fruit-based toppings.