Sprinkle strawberries with 1/2 cup sugar in a heatproof bowl; set aside.
Place zest in a medium saucepan, cover with cold water, and bring to a boil. Strain and discard water; set zest aside. Bring 1/2 cup water and remaining sugar to a simmer in saucepan. Add zest, and simmer until mixture is syrupy (about 20 minutes).
Strain zest and reserve, pouring remaining syrup over strawberries. Coarsely mash berries, and return to saucepan. Simmer, skimming foam and stirring occasionally, until mixture is darker in color and slightly thickened (about 45 minutes). Stir in zest; cool. Add lemon juice to taste. Store in a covered container; refrigerate up to 10 days.