Bring 4 cups of water to a rolling boil. Remove from the heat, add the 6–7 Lipton tea bags, cover, and let steep for 30-45 minutes.
In a large skillet, combine the canned peaches (with their syrup), the fresh peach slices, ⅓ cup of the sugar, the cinnamon, and 1 cup of water. Reserve the remaining sugar for sweetening the tea. Bring the mixture to a gentle simmer over medium heat and cook for 8–10 minutes, stirring occasionally. Lightly mash the peaches with the potato maser or use back of a spoon to release even more flavor.
Place a fine-mesh strainer over a bowl or measuring cup and carefully pour the peach mixture through it. Press gently on the peaches with the back of a spoon to extract as much flavorful syrup as possible. Discard the solids or save them for another use.
Remove the tea bags and pour the brewed tea into a 1-gallon pitcher. While the tea is still hot, stir in the strained peach syrup and the remaining 4⅙ cups of sugar add one cup at a time taste as you GO ADJUST TO YOUR TASTE.
Fill the pitcher with cold water until full and stir well. Add a handful of fresh peach slices directly to the pitcher.
Refrigerate for at least 30 minutes. For the richest peach flavor, let the tea chill and infuse for 1–2 hours before serving.
Pour over ice and garnish with additional fresh Lemon slices.