Hull and quarter the strawberries. Place the strawberries in a large bowl. Stir in the sugar and ¼ cup lemon juice. Allow to sit, covered, for 30 minutes.
In a countertop blender, blend the strawberry mixture until pureed. Strain the mixture through a fine mesh sieve to get the seeds out.
In a large pitcher, combine the strawberry puree with the remaining 1 ¾ cups of lemon juice and 4 cups of water. Add up to 1 additional cup of water to taste if the mixture is too sweet or strong.
To serve, stir the lemonade and pour it over ice. Garnish with lemon slices and strawberries.