Stir together strawberries and sugar in a large bowl; crush strawberries with a wooden spoon, and let stand at room temperature 30 minutes.
Process strawberry mixture in a blender or food processor until smooth, stopping to scrape down sides as needed. Press mixture through a wire-mesh strainer into a large pitcher, using back of spoon to squeeze out juice; discard solids. Add cold unsweetened tea and lime juice, stirring until blended. Cover and chill 2 to 24 hours.