To Make the Ice
In a medium saucepan, bring 1½ cups of the water to a boil. Turn off the heat, add the tea, cover, and let steep for 5 minutes. Strain the tea, discarding the tea leaves, into a bowl. Stir in the sugar and let cool to room temperature. Stir in the lemon juice, the remaining 1½ cups water, and the salt. Refrigerate until cold, about 2 hours or up to overnight. Churn in an ice cream machine according to the manufacturer’s instructions. For a smoother texture, freeze until scoopable, about 2 hours. For an icier texture, freeze until hard, 6 hours to overnight, and break it up with the end of a spoon or the tines of a fork. In either case, serve in bowls with the berries.
The ice can be made 2 days in advance.